The 30-year-old will join Rhinos for the 2022 season on a one-year contract.
Born in Australia, Austin played for Great Britain on their southern hemisphere tour two years ago.
He is Rhinos' third signing for next season, alongside Huddersfield Giants half-back Aidan Sezer and second-rower James Bentley from St Helens.
Austin, who was a try scorer in the Wolves' 27-26 win at Leeds last Sunday, said he is "stoked" to be joining Rhinos.
"While I have some disappointment at leaving Warrington, I’m extremely happy to be joining such a great club," he said.
"Leeds are a club I set my sights on a few months back and I’m stoked to be getting on board.
"I’m joining one of my best mates and a squad that look set for an exciting next five to 10 years."
He added: "I opted for a one-year deal to prove myself to the Leeds faithful, but I also believe it’s something that will help get the best out me personally.
"I definitely want to settle in for a lot longer.”
Austin has played in the halves for Warrington, where he has made 62 appearances in three seasons, but will take a utility role at Leeds.
Rhinos coach Richard Agar said: “We are delighted to be able to add a player of the quality of Blake Austin to our existing squad for next season.
"Consistently over the last two seasons, we have spoken about creating competition for every position in the side and, just as importantly, making sure that we have strength in depth.
"We saw earlier this season that we needed to improve our options at half back, which Blake will certainly do but he can also play a number of positions across the team."
Agar added: “We see plenty of adaptability and versatility in Blake and, of course, he has a great deal of experience both in the NRL and Super League, having played nearly 200 games.
"Throughout our discussions about our vision for his role within our squad, I have been impressed with his ambition and willingness to play his part for the team and I am looking forward to seeing him in our environment."
Austin played alongside Sezer for Canberra Raiders between 2016 and 2018.
He began his NRL career at Penrith Panthers in 2011 and then had a spell at Wests Tigers, alongside Rhinos forward Bodene Thompson.
He joined Warrington in 2019 and was a Man of Steel runner-up that year.