Mama, currently at Sixways on loan, is next season's fourth signing following lock forward Will Spencer and centres Ben Te'o and Jackson Willison.
But Mama, 24, will spend the last three months of this season back at Bristol.
He will return to his current parent club on 28 February before rejoining Premiership side Worcester next season.
"I think I've made some huge strides playing for Warriors in the last few months," he said. "But I've enjoyed some good times with Bristol and I will give my all to help them try to get promoted."
Mama, who came through Bristol's academy set-up, played against Warriors for their chief promotion rivals in all four of last season's Championship meetings.
He scored an impressive 22 tries in 106 games for Bristol, getting his first Premiership try for Worcester when he crossed in the 24-20 home defeat by Harlequins earlier this month.
Warriors host Exeter on Sunday, when they will hope to end a run of 10 straight defeats in the Premiership and European Challenge Cup.
Warriors have signed winger Dean Hammond on a new, undisclosed-length contract.
The former South African Under-20 international made 15 appearances in his debut season after signing in September 2013 following a successful trial at Sixways.
Despite an injury-hit 2014/15 campaign, he then ran in seven tries in 11 appearances last season, helping Warriors to win the British & Irish Cup, as well as scoring a key try in the Championship semi-final second leg win over London Scottish.
"I've made some great friends since moving to the club and have grown very fond of Worcester," said Hammond. "I'm looking forward to the future at Sixways and hope I can help us build something really special."
Warriors director of rugby Dean Ryan said: "Dean is a young player who has developed immensely. He has not been fazed by the amount of competition for places."
Worcester have completed the signing of Bristol loose forward Marco Mama, who has signed on an undisclosed-length contract ahead of the 2016-17 season.