The 24-year-old - who qualifies for Scotland courtesy of his Dumfries-born grandmother - moves to Scotstoun following a one-year stint at Racing 92, making 25 appearances across all competitions.
Equally comfortable at both fly-half and in the centres, Lancaster scored 57 points for the Parisian outfit, starting 12 times in the Top14 and featuring in all bar one of the club's European fixtures across the Investec Champions Cup and EPCR Challenge Cup.
Lancaster previously represented Ealing Trailfinders and Leicester Tigers. He made his senior debut for Yorkshire Carnegie after starting out at West Park RFC.
The Leeds-born pivot also represented Bond University in the Queensland Premier Rugby competition, enjoying a two-season spell on Australia's Gold Coast.
He represented Scotland at U18 level, lining up alongside future team-mates such as Jamie Dobie and Ollie Smith in the dark blue jersey.