The name "Rigellian" was introduced to the world nearly a full six months before the release of The Motion Picture. During her visit to the set of The Motion Picture, Susan Sackett noted many "curious creatures", including the "reptilian Rigellians". (Starlog #23, June 1979, p. 31.)
The Rigellians were designed by Fred Phillips and Robert Fletcher for The Motion Picture. With the approval of Gene Roddenberry, the Rigellians, as well as numerous other new species in the film, were named by Fletcher and provided a backstory by him. The following is a brief description, in Fletcher's own words:
"RIGELLIANS – Descended from race of saber-toothed turtles, learned to walk upright. Range from five nine to seven feet and over. Unisex. Lay eggs. Real power is with attendants who serve, feed, and care for them. Costume of draped wool. Hands and feet of sculpted rubber. Wear ceremonial helmet and half-armor. Armor sculpted in studio craft shop, molded Fiberglas and chrome-plated." (The Making of Star Trek: The Motion Picture, p. 132)
"Don't let their size – 5'9" to 7' – or their heritage – descendants of a race of sabre-toothed turtles – overwhelm you, they are basically a peaceful race. What appears to be war-like armor plating is in fact a manufactured exoskeleton because the poor turtles have lost their shells. Although the larger of the species are called the Lords and are catered to hand and foot [?] by the smaller attendants, it is in fact the attendants who hold the real power." 
In an interview appearing in the March 1980 edition of Fantastic Films, part two of "The Star Trek Costumes", Fletcher revealed more information about the Rigellians and the design of their costumes:
"This is the Rigellian Lord. They are a race of spacegoing turtles who no longer have shells to support their bodies. The material in his costume is a knit. The draping and coloration of the armor plating makes him a very elegant fellow. The armor plating was sculpted in the studio craft shop and is really fiberglass that has been chrome plated.
"The Rigellian Lord is a very tall creature and his attendant is a smaller creature but physically the same. His costume is very similar to the first Regellian but a little less regal in appearance. The standard he is carrying was done by Tom and Maggie Browne and it's a carving representing his master's household crest and position in the community. The first Rigellian is not really the master. You see, the large turtles are the egg carriers and the smaller ones are the real power in the community. I guess you would call the Lord a figurehead."
In an article appearing in the January 2002 edition of Star Trek: The Magazine Volume 2, Issue 9, entitled "Who is that Alien?", the following information about the Rigellians, which included information taken from Fletcher's original background notes, added:
"Believe it or not, the Rigellians were supposedly descended from a race of saber-toothed turtles. They only had one gender and reproduced by laying eggs. Their armor was principally ceremonial, and the real power lay with their attendants who gave them food."