The 26-year old back-rower, who has also played lock for the region, was out of contract at the end of the season, and will link up with former Osprey Jonathan Spratt at the Madejski Stadium next season.
Since making his debut against Connacht back in February 2007, Smith has made 83 Ospreys appearances, scoring two tries.
Speaking after his move was announced, Smith commented:
"Obviously it's sad to be leaving my home region, and it was a very difficult decision to make, but I feel that the time is right for me personally to move on for a fresh challenge.
"I've always been proud to be an Osprey and the region will always be my home but it's the nature of professional sport that people don't stay in one place. I've got a lot of good friends who will still be here, and I'd like to thank all the players, coaches, management and fans for all the support I've had as an Osprey.
"We've got a lot still to play for in the league this season and I'll be looking to leave on a high."
Guinness PRO12
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