(written from a Production point of view)
A new, retconned CGI studio model for the Constitution-class, designed by John Eaves, was introduced in the first season finale for Star Trek: Discovery, "Will You Take My Hand?". The retcon design was said to bring the USS Enterprise more in line with Federation aesthetics as seen in Star Trek: Enterprise and Star Trek: The Motion Picture, even though the original Matt Jefferies design was used for the USS Defiant in the Enterprise season 4 episodes "In a Mirror, Darkly" and "In a Mirror, Darkly, Part II", and in the Discovery episode "Despite Yourself" earlier in the first season, albeit as a slightly modified wire-frame graphic only. 
Moreover, an adapted Original Series configuration along Jefferies' classic lines was seen more prominently on a computer display as Enterprise itself in the second season episode "Brother", when the ship's files were being accessed.
The episode was set in 2257, after the events of the original Star Trek pilot "The Cage", but before the events of the second pilot for The Original Series, "Where No Man Has Gone Before". The retcon design is intended for 21st century audiences as a modernized version of the original "classic" design within the prime timeline, and consequently meant to be one and the same in canon.  The redesign does away with the classic smooth hull look and adds detail such as phaser ball turrets and photon torpedo launchers. The saucer was also slightly changed adding in a larger aft section, housing the impulse engines. The ship was also upscaled from its original size. (Star Trek: The Official Starships Collection, Issue XL11, p. 16)
According to an article entitled "Designing The Enterprise" included in the booklet accompanying the Eaglemoss model of the ship (Star Trek: The Official Starships Collection, Issue XL11, pp. 6-19), the task of redesigning the vessel was initially assigned to John Eaves, in collaboration with Scott Schneider and William Budge, by then-production designer Todd Cherniawsky, prior to Cherniawsky being replaced in that capacity by Tamara Deverell, who then continued to oversee the trio's work. After briefly considering a radical departure from previous depictions, the designers instead aimed, in Eaves' words, "to get as close as possible to the original", yet add "the sleek, unique Discovery look to it."
At first Eaves and Schneider stayed very close to the classic lines as set by Matt Jefferies and this version they submitted actually nearly made the cut, before it was decided at the eleventh hour to go for a more radical redesign. Nonetheless, the production designers decided to have a preliminary smooth skinned version of this iteration featured, along with listing dimensions and other specifications copied from Franz Joseph's Star Fleet Technical Manual, as the graphic display in "Brother", intended to be an "Easter egg for the [diehard] fans", as Deverell had put it at the 9 February 2019 Directors Guild of Canada's season one finale screening. 
Having settled on an interpretation that the resulting configuration would be "the same ship that Kirk commanded at an earlier stage of its life, before several refits…that various components such as the warp nacelles or the impulse engines would be replaced over time…they set about designing more primitive versions of them." (Eaglemoss booklet, pp. 7-8) Eaves recalled, "We were trying to do things that implied it could transition to the original Matt Jefferies ship later on…we wanted to create links with ships that had come before…for example, we rotated the exhaust ports on the back of the nacelles 90 degrees inward. On the Phoenix those had faced each other like that." (Eaglemoss booklet, pp. 8-9) Schneider elaborated, "We were constantly trying to tie into both the past and future architecture of Starfleet ships…we tried to tie stuff into the NX-01 and stuff that would come in the future, like the Enterprise-B…in the beginning, we had the ball on the back of the nacelles…later on, we got into a meeting with Tamara…and I said…time-wise we should…put grilles in there instead…we wanted to show some connection to the motion picture refit…get some of those details that you see on the refit in there, but to make it look as if they were in their earlier stages…they've got aft torpedoes here and eventually on the refit they move it to the neck." (Eaglemoss booklet, pp. 9-12)
Schneider said of Budge's role (Eaglemoss booklet, p. 12), "William was constantly keeping us in check…watching over things to make sure we maintained continuity with all the other ships from the Discovery era. There were times when he'd say, 'OK this is great, but we've got established details on the rest of the fleet that we need to carry over." These details included exterior lighting features such as the "wedge" of "segmented lights in front of the bridge" (Eaglemoss booklet, p. 9) and the bridge viewscreen window typical of Discovery-era vessels. To reconcile this window with Jefferies' original design, Schneider devised the idea that the forward part of the bridge superstructure would be made of transparent aluminum, which "during battle would go opaque and during exploration mode…would go transparent", revealing the window. (Eaglemoss booklet, p. 17)
Another Discovery-style feature initially included in their submitted design was "a double-pronged antennae on the front" of the deflector dish. (Eaglemoss booklet, p. 9) This, along with the the nacelle pylons, which, per comments made by Eaves on Facebook, had been "split…so in time the cooling vent side could be removed to make it more like the original TOS strut", with Schneider adding in regard to their original, almost approved design, "We had straight pylons…we never considered the swept [design] because we felt it would be jumping forward in time for one element", and other cosmetic details were further revised by the visual effects team after leaving the hands of the designers. 
In the same Facebook post, subsequently deleted, Eaves reiterated his conception that "the advantage of a ten-year gap in Trek history" allowed them "to retro the ship a bit with elements that could be removed and replaced, somewhere in the time frame of Discovery and The Original Series." Eaves further suggested that the assignment "started with the guideline that the Enterprise for Discovery had to be 25% different" from the original due to issues of "Star Trek ownership" between Paramount Pictures and CBS Television Studios. Schneider, though self-admittedly "know[ing] nothing of copyright law", suggested that this was a "legal" requirement "in order to avoid copyright infringement."  However, after these comments were reported by sources such as ComicBook.com, this claim was refuted by a CBS spokesperson, clarifying that "CBS TV Studios does, in fact, own the rights to the designs for the USS Enterprise seen on previous Star Trek television series", and that "any changes made to the design of the Enterprise were creative ones to utilize 2018 VFX technology." 
Schneider added, "There are extra details that John and I put in that you won't even see in the show…I had photographs of the original model…I was always referring back to them. There are little details. On the original they never actually show where the phaser banks were…where the torpedoes were. They would just magically come out of the hull. So we built all those details in. We put in the RCS thrusters that they didn't have…but which must have been there for the ship to work…we put in a warp core ejection hatch and we put in tractor beams…we put in rear phaser banks…". Eaves elaborated that these functions were assigned to external features intentionally reminiscent of details found on the original model, and that many of the original "call out numbers" applied to various surfaces of the original were included on their submitted version, supplemented by "initials and the birth dates of people that had an influence on the design of the Enterprise", among them Matt Jefferies, Andrew Probert, Doug Drexler, Bill George, and Gene Roddenberry, in addition to Schneider and Budge. However, Eaves expressed doubt that these survived in the final rendition used onscreen. (Eaglemoss booklet, pp. 10-11)
Another nod to the original was included in Schneider's concept for the bridge turbolift (Eaglemoss booklet, p. 18), "You have an elevator shaft on the center line and two standby elevators off to the side. So one would slide back and over and go down the tube and another one would come in. This is why you could get an elevator quickly because there's always at least two standing by and that explained why there is a center shaft."
The size of the ship was an issue of contention during the redesign process. Eaves summarized (Eaglemoss booklet, p. 16), "The scale would go up and down…were we going to keep the scale of the original scenes or was it going to be increased to match the size of the Discovery ships…it was decided we were going to go with the 1500-foot scale range so the windows had to be adjusted, but we still tried to keep that TOS pattern of what the windows looked like." Deverell stated at the 2018 WonderCon event, "Overall, I think we expanded the length of it to be within the world of our Discovery, which is bigger, so we did cheat it as a larger ship."   
Derivative physical models Edit
While a physical studio model is not utilized as a production asset for Discovery, the CGI meshes created for the show were nonetheless utilized as masters in order to bring the retcon Constitution-class model into the physical realm as merchandise, most notably display models.
In January 2018, Eaglemoss Collections' Hero Collector brand premiered the Star Trek: Discovery The Official Starships Collection partwork which featured the retcon USS Enterprise in March 2019 as the regular issue 12. Nonetheless, a larger version of the model was in December 2018 first released in the mother publication Star Trek: The Official Starships Collection as issue XL11. Created in Pixomondo's Autodesk Maya software, the production CGI model, which served as the computer template from which the display models were constructed, needed conversion into LightWave 3D, Eaglemoss' software package of choice for their publications, which was entrusted to Fabio Passaro.