His deal was set to expire at the end of the upcoming season. The Athletic understands that the option includes a substantial pay rise.
Gilmour was signed from Rangers by Chelsea for a £500,000 fee at 16, and made his debut two years later in 2019.
He has made 22 Chelsea appearances across all competitions, but these predominantly came under previous head coach Frank Lampard, with Gilmour starting only three games under Thomas Tuchel.
The central midfielder faces competition from N’Golo Kante, Jorginho, Mateo Kovacic, Ruben Loftus-Cheek, and Ross Barkley, as well as Conor Gallagher, who has returned from a season-long loan to Crystal Palace.
However, Gilmour is highly rated, with The Athletic revealing last year how Tuchel played a central role in choosing where the youngster would go on loan.
(Photo: Darren Walsh/Chelsea FC via Getty Images)