Cox first arrived from Sale Sharks on a one-year deal in 2011 before earning a two-year extension the following season.
He will leave to join London Irish having made 61 appearances for the club to date.
Edinburgh Rugby head coach Alan Solomons, said: "Sean [Cox] has been an integral part of our club for three years now and has made a valuable contribution."
"We wish him all the best for the future."
Cox said: "I've had some incredible highlights at Edinburgh Rugby and want to thank the club for the last three seasons."
"I'm delighted to be joining London Irish next season. I'm looking forward to the challenge and being back in the Premiership."
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