The 30-year-old will continue to assist Glasgow's bid to reach the RaboDirect PRO12 play-offs before moving to Sixways in the summer.
Lemi arrived at Scotstoun Stadium last November, and has since featured in six RaboDirect PRO12 games.
Head coach Sean Lineen today paid tribute to the Samoan international's professionalism, and hailed the strength in depth in the Warriors back three.
Lineed told www.glasgowwarriors.org: "David has had a positive influence on and off the field through the manner in which he's conducted himself.
"When DTH van der Merwe injured his shoulder, we needed a good quality replacement, and David has stepped in the breach very capably.
"DTH is progressing well in his rehabilitation, and we're very happy with the back three options we've got going forward.
"Stuart Hogg is getting more and more impressive all the time, Peter Murchie and Tommy Seymour have really been coming onto a game of late, and Colin Shaw and Federico Aramburu have both scored important tries.
"Rory Lamont has done well since returning to the club, and we've got Sean coming in next season too. We're looking strong in that part of the team, and we're very hopeful of adding players in other areas in the near future."
Lemi said: "I would like to thank Glasgow Warriors and Scottish Rugby for the wonderful opportunity I've been given this season. I've really enjoyed my time in Glasgow as part of a fantastic squad of players under a strong management team.
"We are in a good position in the RaboDirect PRO12 and I remain totally committed to helping Glasgow reach the play-offs and make this season a successful one before I make the move to Worcester."
In addition to securing the return of Sean Lamont, Glasgow Warriors have made 12 long-term re-signings ahead of next season. Ed Kalman became the latest star to put pen to paper yesterday, 24 hours after making his Scotland debut in the RBS 6 Nations match against Wales in Cardiff.
Guinness PRO12
Suite 208, Alexandra House,
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