The 29-year-old has moved to Villa Park from Fulham on a two-year deal.
Richardson has said that the presence of former Manchester United teammate and Sunderland boss Keane played a big part in his decision to join the club.
"That season when I signed for Sunderland I think I only played 10 games because I had a hairline fracture in the L5 vertebrae in my spine," Richardson told Clubcall.com.
"Throughout that season I was very upset, I put on a lot of weight and I got bigger. But just before the end of that season, Roy took me into his office and we had a massive conversation.
"He inspired me to go away in the summer and come back in better shape than I had ever been in. I went and played very well in the next season. He gave me some good words of encouragement to go and do that over the summer and I appreciate that."
Richardson is Villa's third signing of the summer transfer window.