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The Blues had been keen to keep the midfielder, who has been tipped for a bright future, but he had been unwilling to put pen to paper on a contract extension after holding talks with the club.
Bate’s deal was due to expire in a year’s time and, as a result, Chelsea have reluctantly elected to sell him.
Leeds have agreed a deal for the 18-year-old worth around £1.5m, but it does include a sell-on clause for Chelsea too.
The youngster will hope to compete for a place in Marcelo Bielsa’s side, with the prospect of first-team football a key factor in his decision to leave Stamford Bridge and take on a new challenge elsewhere.
Bate has signed a three-year-deal at Elland Road, running until the summer of 2024, and will initially link up with their Under-23s for the forthcoming season.