Hooper, who has won 10 caps and was part of Australia's 2023 World Cup squad, will link up with former Brumbies team-mates Scott Sio and Tamati Tua at Sandy Park.
Hooper, who came through the Brumbies Pathway programme, told the Canberra club's website: "My biggest focus this year is a short-term goal and that is winning Super Rugby Pacific with the ACT Brumbies.
"I want to send off my stint in Canberra in the best possible way and that's by giving the fans exactly what they deserve, another Premiership. I am going to do everything in my power to make sure that happens."
"Across my five seasons as a Brumby, the club and Canberra have become my home. Unfortunately, with the changing dynamic of rugby, sometimes you must fly the coup. That's what I'm going to be doing next season.
"I'm going to leave the Brumbies and try my best to become a better player, with a view to coming back to Australia and becoming an older, more experienced player later down the track, whenever that may be."
The 23-year-old leaves just as his 20-year-old brother Lachlan is pushing for a plce in the Brumbies first team.
"We are delighted to have signed Tom. We see him having the opportunity to play across our back row, but cover second row as well," Chiefs rugby director Rob Baxter said.
"He has got a lot of the attributes that are really important in Premiership rugby - high work-rate, along with good physical size and good physical abilities.
"He is also an interesting character, and someone we are excited to bring to the club to grow the team we want to put together going forward."
It has been reported Hooper will double his salary in England.
Director of High Performance at Rugby Australia Peter Horne said: "Tom has been presented with a good opportunity to play overseas next season. Rugby Australia thanks him for his service to Australian rugby and wishes him all the best for the future."
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