The Tongan signed for the Warriors last September but his short-term deal expires at the end of the season.
He has now agreed a two-year deal with Worcester, where he will join up with Scotland front-row forward Euan Murray.
Fainga'anuku has so far made 11 appearances for Glasgow and played the full 80 minutes in the recent 20-14 RaboDirect PRO12 victory over Ulster.
Glasgow head coach Gregor Townsend said: "We would like to thank Ofa for everything he has done for the club both on and off the pitch.
"He has fitted in really well in the short time that he has been here and this is a fantastic move for him and his family.
"He is fully focused and committed to us until the end of the season and we are very happy that we'll be able to call upon his services until then."
Fainga'anuku added: "I've really enjoyed my time in Glasgow and I'd like to thank everyone at the club for their help and support.
"I am looking forward to being involved in the remaining games this season and contributing to what we hope will be a successful end to the campaign."
- Sports & Recreation