Tonks made 77 appearances for the Scottish club and has earned six caps for his country including three during last year’s RBS Six Nations.
Tonks told edinburghrugby.org: “I loved my time at the club, and Edinburgh has become a home for me. I’m very sad to leave, but the opportunity came up for a change of scenery and I wanted to give it a shot.
“I’ll leave Edinburgh with a lot of good memories. I spent four years with very good people, good friends, and I’ve got huge respect for the coaches and all the staff involved.
“I feel that I leave the club in the best position it’s been since I started, and I wish everyone at Edinburgh the best for the future.”
Head coach Alan Solomons said: “Greig has been a valuable member of the Edinburgh team over the past four seasons and we wish him all the best in his new challenge.”
Edinburgh’s Pro12 rivals Ospreys, meanwhile, have signed Crusaders back Kieron Fonotia for next season.
The move, subject to a work permit, will see the 28-year-old centre or wing switch to the Liberty Stadium on a two-year deal. Christchurch-born Fonotia made his Super Rugby debut at the start of the 2014 season and has played more than 20 games for the New Zealand side.
Ospreys general manager Andrew Millward said: “We are delighted to be able to announce the signing of a player who has made a huge impact in Super Rugby over the last few years alongside some of world rugby’s most exciting backs, and whose versatility will make him a huge asset for us over the coming seasons.
“He will bring a positive mindset and a willingness to challenge defenders with a dynamism and skill set that can grow our game and complement the players around him.”