Hines, who won his 31st cap for Scotland in last weekend's Calcutta Cup match, has played 90 games for Edinburgh.
Edinburgh Rugby head coach Frank Hadden said: "We are saddened to lose Nathan's services. He has been influential in the development of Edinburgh's game over the last four years especially and we hope that some of our young players will step into his shoes as quickly as possible. We wish him well.
Hines' fellow forward, Edinburgh Rugby captain Todd Blackadder, said: "I will miss him firstly as a mate - I think we all will. He has a great attitude and is a wonderful personality.
"He possesses skills which we don't have in abundance in Scotland. We'll miss both him and Leann and wish them all the best for their new life in France."
Hines said: "I'm sad to leave because I have been here in Scotland for seven years - which is six-and-a-half years longer than I was intending to stay. The reason for that? I like the country and I like the people.
"I have had a really good time since I've been here and I've enjoyed the opportunities that have come my way. My move to Perpignan is another one of those golden opportunities that I cannot pass up.
"I also want to thank the Edinburgh supporters and the people of Scotland for treating me as if I was brought up here because that's made a big difference to me and Leann (his wife).
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