Tigers acting head coach Richard Cockerill said: “We have had to make some very tough decisions in light of the current market, with players’ wages getting higher and higher, and a salary cap in force. But we have only got so much room at the table.
“Tom’s service to the club has been enormous and, even in difficult times, his attitude has been first class.
“It is disappointing that Tom has to move on. It is not ideal, but you have to make tough decisions.
“He has come through the system here, he has done some fantastic things for the club and we wish him all the best.”
Varndell said: "The move to Wasps offers me a new challenge in a new environment and, speaking to Lawrence Dallaglio, Ian McGeechan and Shaun Edwards as well as current players, there is a really good feeling at the club despite a pretty tough season.”