Wasps meet Biarritz in the last eight at Adams on Saturday, 7 April, while Cardiff Blues travel to the Aviva Stadium in Dublin to take on Leinster in the Heineken Cup quarter-final on the same day.
London Wasps Director of Rugby Dai Young said: "I obviously know Rhys very well having coached him for many years and he will be a real asset to our squad next season. He is an experienced international and exactly the kind of quality player we want to bring to the Club. Rhys is also a great guy to have around a squad and he will be a great addition to the Club off the pitch as well."
Thomas said: "I am really looking forward to linking up with Dai Young again who has been a big influence to me in my career and I'm excited by the challenge of playing in England with London Wasps. Like most professional players I always keep an eye on how the game is going in England and it's the kind of challenge that I know I will relish."
Thomas is one of a number of senior international players having signed on at Wasps for next season with England's James Haskell and Tom Palmer also joining Young's squad later this year.