Richardson was dismissed by Illinois State earlier this year after posting a 56-64 record over the last four seasons, including an 8-21 mark in 2002-03.
"Kevin's the one who got me into college coaching and now he's keeping me in it," Richardson told the Bloomington (Ill.) Pantagraph. "Kevin basically offered me this job the night I was fired. I appreciate his friendship and I'm looking forward to getting back with Kevin and helping Vanderbilt.
"I looked at some different things, but felt this would be the best opportunity for me and my family. I'm not exactly sure what my duties will be, but I'll be involved in all aspects of the program."
Stallings lost his top assistant, Tim Jankovich, to the University of Illinois in November, 2002, only days before the season opener, and had not filled the open position. Jankovich left to join the staff of Bill Self at Illinois, and later followed Self to Kansas University when Self was hired to succeed Roy Williams.
"Tom is the best coach I've had on staff in terms of a guy who has been an assistant for me," Stallings told The Pantagraph. "I'm just sorry the circumstances were such that I got him back. I know Tom is looking forward to working with people who will treat him well.
"Tom and I work well together because philosophically we see the game the same way. He's a very, very bright basketball coach and a guy who is very loyal and hard working. He has every ingredient you want in a person on your staff.
"We think we'll be a better team this year," said Stallings. "We have just about everybody back from last year. We need to be better. We'd better be better."
With Richardson as an assistant from 1993-99, Stallings guided the Redbirds to one of the most successful eras in school history. The team went 123-63 with two Missouri Valley Conference regular-season titles, two post-season conference tournament crowns, two trips to the NCAA Tournament and two to the NIT.
Before coming to Illinois State, Richardson was 193-146 in 13 seasons as head coach at Nazareth Academy High School in LaGrange, Ill. He began his coaching career at his high school alma mater, Marist, in Chicago, where he was an assistant from 1977-79.
Another current Stallings assistant, Dan Muller, played for both Stallings and Richardson at Illinois State.
Richardson is married and has three children, two of whom are students at ISU.