The 30-year-old, who has been capped by Australia in rugby union and Tonga in rugby league, has made six appearances since originally joining in January.
Vuna initially agreed a deal until the end of the current campaign but he will now stay at The Rec next term too.
He said on the club's website: "I've really enjoyed my time here so far, and I'm looking forward to getting a full season under my belt.
"There's a real hunger and desire to be successful here, and have no doubt that with the players and support staff we've got behind us, we can do just that."
Director of Rugby Todd Blackadder is also pleased with the news and says the new deal is just reward for Vuna's performances on the pitch and the impact he has also had in the dressing room.
He said: "Cooper is a great influence around the place - the way he conducts himself on and off the field is second to none.
"Cooper has worked really hard on his game since he's been here, and we're now reaping the rewards. He's got a real eye for the try line and given half a chance, you know that he's going to take it."