The 17-year-old announced the deal on his Twitter with pictures of him with his family as he signed the contract.
Gilmour moved to Stamford Bridge from Rangers a year ago after rejecting an offer to stay at Ibrox.
The midfielder impressed for Chelsea’s Under-18s last season and he carried that form into the Toulon Tournament in June for Scotland. Gilmour won the tournament’s breakthrough player award, while he was selected in the team of the tournament.
He is expected to feature for Chelsea’s under-23 side in the Premier League 2 this coming season.
Former Hibs and Ranger midfielder Kevin Thomson congratulated Gilmour on his new contract on Twitter.
He wrote: “Well done buddy!! Keep up hard work!! Keep believing!!! Desire drive determination to be the best you can be!!!”