The 27-year-old will become the highest paid player in England on a two-year deal worth 1.5 million pounds ($2.15 million), according to British media reports.
Wasps announced the deal on their website (www.wasps.co.uk) on Friday, with Beale's future having been the subject of intense media speculation all season.
Beale, known for his versatility in the back row, has 60 caps to his name and played a key role in his country's run to the 2015 Rugby World Cup final.
"The passion for the game in Europe is huge and I want to be a part of it... I want to win trophies with Wasps in the Premiership and Europe, and continue playing for the Wallabies," Beale said.
Beale would still be eligible to play for Australia, having featured in 60 tests for the national side.
Beale's Waratahs and Wallabies team mate Michael Hooper had said before the deal was confirmed that it would leave a large hole for the Waratahs to fill next season.
"You can't replace Kurtley Beale," Hooper said. "You get something different and that's with rugby what we'll be chasing.
"I'm happy for him as an individual. The ability to make those decisions is all part of rugby but, for me, selfishly it's probably disappointing."
Beale returned to the Waratahs in 2014 after being sacked by the Melbourne Rebels in the wake of a series of incidents, including punching his captain Gareth Delve on the team bus.
Beale becomes Wasps' eighth signing for next season, joining Guy Armitage, Danny Cipriani, Tom Cruse, Marcus Garratt, Marty Moore, Tommy Taylor and Tom Woolstencroft.
($1 = 0.6971 pounds)