The Whites are understood to have agreed a £1.2m fee for the 18-year-old, who was also interesting West Ham United and Liverpool.
Bate has signed a three-year contract to be part of the club's concerted plan to sign some of the country's leading young players. Shaun McGurk and Amari Miller have already joined this summer, following on from the likes of Sam Greenwood, Joe Gelhardt, Charlie Allen and Cody Drameh last year.
Leeds have said he will initially join up with the under-23s rather than the seniors.
Bate spent 10 years in Chelsea s academy, the best in the country, but was sold after he refused a new contract, with his present deal entering its final 12 months.
He captained Chelsea in last season's FA Youth Cup final, and played more minutes than anyone as the young Blues finished as runners-up to Manchester City in Premier League 2 Division 1, the country's leading under-23 competition which has taken the place of reserve team football. Bate is also an England under-17 and under-18 international.
After winning promotion to the Premier League last season, Leeds embarked on a double-pronged transfer policy with a large number of junior signing topped off by some very targeted first-team additions to provide top international quality in specific positions. It seems likely to be the case again this season with left-back Junior Firpo the only new first-teamer to date, and Jack Harrison's loan from Manchester City made permanent. The only difference this year is that after loaning Kiko Casilla to Elche, they are expected to target a young goalkeeper to back up Illan Meslier in the first-team squad.
In their debut season, Leeds were the Premier League 2 Division 2 champions under new manager Mark Jackson. His predecessor Carlos Corberan left to become Huddersfield Town's head coach at the end of the 2019-2020 season.
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