The 20-year-old has been involved in all three of Glasgow’s recent Rainbow Cup matches and made his first start for the Warriors in the impressive 31-24 win over Edinburgh at BT Murrayfield last weekend.
His performance drew praise from head coach Danny Wilson who believes the loosehead has earned his deal.
“Tom has really proved himself in recent weeks,” said Wilson.
“He's a good, young prospect who's been willing to put in the hard work off the pitch throughout the season to develop his game and has earned the opportunities he’s had against Edinburgh and Benetton.
“It’s great to see another academy member turn professional and we looking forward to seeing more of him in a Glasgow jersey next season.”
Lambert is a former Sydney University student and represented Australia at under-19 level. He joined the FOSROC Scottish Rugby Academy at Scotstoun in the summer of 2020 and switched his allegiance to Scotland and was capped in the 2020 U20 Six Nations.
He said: “Coming from Australia at the start of the season, the boys have made the transition really easy. It’s an awesome club, a really good group with great values that like to train really hard on the pitch and have a laugh together off it.
“I’m really hungry to play more rugby - I’ve had a taste of what it is like to play for Glasgow this season and my main focus now is to keep playing and competing for my place in the 23.”