The 6ft 5in, 130kg tighthead prop joined Leinster two years ago and to date has made 11 appearances for the province's 'A' side, including seven in the British & Irish Cup.
Maguire has also represented Ireland at Under-20 level and was a member of the Six Nations-winning team of 2010.
He played in last summer's IRB Junior World Championship in Argentina where he lined out with Connacht trio Eoin Griffin, Tiernan O'Halloran and Denis Buckley.
This season, the 21-year-old front rower has been part of Old Belvedere's challenge for Ulster Bank League Division 1 honours.
"I have thoroughly enjoyed my two years at Leinster, where the coaching staff have improved my fitness and level of play enormously, and helped me to be an important part of Ireland Under-20 side last season.
"However, I feel that I now need exposure to regular rugby at a higher level, and Connacht's coaching staff convinced me that I can have a big role to play in their matchday squad next season."
Connacht assistant and forwards coach Dan McFarland said: "We're really looking forward to working with Stewart, he has good potential as a scrummager and is a dynamic ball carrier, having played well for the Ireland Under-20s last season.
"He has not been able to get senior game-time at Leinster and is coming here with a real point to prove. We believe we can offer him the best possible opportunity to showcase his talents.
"We are confident he will fit comfortably into our set-up as we build our squad for next season."