Spurs have come to believe that despite late interest from Manchester United, Ndombele wants to join them.
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His arrival at Elland Road follows that of defender Ben White from Brighton and Hove Albion and a loan deal to keep winger Jack Clarke at the club after he was transferred to Tottenham.
A surprise U-turn has seen Spurs change their mind on loaning Clarke back to Leeds as part of the deal, while the Daily Telegraph says Wolves winger Helder Costa will also complete a loan move to the Championship side on Monday.
He's the first player to join Spurs since Lucas Moura switched from PSG 18 months ago.
Ndombele made 49 appearances for Lyon last season, including eight Champions League starts, scoring three goals.
The deal for Ndombele, who has agreed a six-year contract, could eventually be worth 70 million euros (£62.77million), according to the French club.
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Given his huge fee, Ndombele is likely to go straight into Pochettino's preferred starting line-up.
With that in mind, Harry Winks and Moussa Sissoko will be forced to work even harder to keep their places in the team.
The 18-year-old made 25 appearances for Leeds last season after coming through their youth ranks and is highly rated so he should prove to be an excellent long-term addition to the Tottenham squad. Pochettino has convinced him that the next step of his career would be best served at Spurs and Ndombele was impressed when shown around the training ground.