The 32-year-old has penned a three-year deal to join the Wycombe based club from Leeds.
"I'm excited about the chance to play with Wasps for the next few seasons - I've been really impressed with some of their young players," said Thompson.
"I'm looking forward to being part of a team that is aiming to get back to the top of their game."
The 2003 England World Cup-winner retired in 2007 because of a serious neck injury but has battled back to fitness and reclaimed a place in the national set-up.
The former Northampton Saint had to pay back a £500,000 insurance pay-out he received when returned to action with Brive in 2007 before re-joining Leeds at the beginning of the current season.
"As much as it has been a difficult season for Leeds on the pitch, I have really enjoyed my time there and met some great people," said Thompson.
"I am very grateful that they gave me the opportunity to return to the English game."
Thompson made six appearances for the Lions during the 2005 tour of New Zealand and Wasps chief executive Chris Thomas reckons the 66-cap hooker is the perfect fit for the Aviva Premiership club.
"Steve is exactly the type of front-row forward we have been looking for in our recruitment drive for next season," said Thomas.
"He will bring with him excellent experience at international and Premiership level and we believe that Steve will also play a big role in developing some of our future talent."