Tonks joined the club from Northampton Saints in the 2012/13 season, and made his debut against Munster that same campaign.
The full-back/stand-off became a regular and made 79 appearances for Edinburgh, scoring 99 points.
He went on to make his international debut for Scotland against Samoa on the 2013 summer tour, and has earned a further five caps, including three in last year’s RBS Six Nations Championship.
Tonks said: “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.”