Narraway, who was made captain at the start of this season, said: "It will be strange to leave because Gloucester has been my only club.
"But moving is going to be a tremendous experience on and off the pitch."
He added: "I've obviously still got unfinished business here in a Gloucester shirt, but would like to thank everyone who has helped me to get where I am today.
"I will miss the club, I'll miss Kingsholm and, of course, the amazing supporters. Gloucester's will always be the first result I look out for and I wish them every success in the future."
Narraway has made more than 150 appearances for Gloucester and has also won seven caps for England, making his debut against Wales in 2008 with his most recent appearance coming in 2009 against Ireland at Croke Park.
Gloucester coach Bryan Redpath said: "Luke has been a fine player for Gloucester and I know he has enjoyed the challenge of captaincy this season.
"He's been with us for a long time but it's the nature of the game that people move on to pastures new. I think he'll do well in France and will go with our best wishes."
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