Mount spent last season on loan at Derby County, excelling under Frank Lampard, who has since taken over at Chelsea.
The 20 year-old's spell at Derby came after a season-long loan at Vitesse in 2017-2018, with Mount netting 14 league goals from 32 Eredivisie appearances.
With Lampard and Mount enjoying a good relationship at Pride Park, and Chelsea serving a two-window transfer ban, the playmaker looks set to play a part for the Blues next season.
"It's a massively proud moment for myself and my family," Mount, who joined the club in 2005, told Chelsea's official website. "I joined this club at six years old and it was always my goal to play for the first team one day.
"I'm really looking forward to the coming season now and working hard to have an impact here at Chelsea. I've been at the club for a long time already and hopefully I'll stay for a long time to come."