Wynne, a member of the BT Sport Scottish Rugby Academy, made his debut off the bench in the Warriors' opening Pro12 match at Connacht.
He has featured in 10 games in the current campaign, making four starts.
Fellow Academy flanker Matt Smith, also 20, has been given a one-and-a-half-year deal with the club until May 2018.
Smith, who plays for Glasgow Hawks in the Premiership but has yet to make his Warriors debut, has scored three tries in nine appearances for Scotland's U20s.
After their back-to-back European Champions Cup victories over racing 92, Glasgow are preparing for their Pro12 derby against Edinburgh at Murrayfield on Boxing Day.
Glasgow have rewarded 20-year-old back-rower Lewis Wynne for his progress this season with a two-and-a-half-year professional contract until May 2019.