The Eagles' interest in Graham had been reported by AFL.com.au for some time, with the Tigers lifting their original contract offer to four years to try and keep hold of the 26-year-old.
However, Graham has opted to move to the Eagles on a four-year deal.
As an unrestricted free agent, the Eagles are not required to trade for Graham, but his age, salary and the length of his contract will all be taken into account by the League when working out Richmond's draft compensation.
"I'm just so grateful for the Richmond Football Club for giving me the opportunity eight years ago," Graham said.
"I have met some amazing people along this journey, and it is tough ... but it is something that I thought I needed for myself. A new chapter and a new challenge.
"Jordy and I are very excited by that, but at the same time, it is sad to say goodbye to so many good people."
https://www.afl.com.au/news/1236224/two-flag-tigers-move-to-eagles-confirmed