The highly-rated 18-year-old, who burst onto the scene at Elland Road last season, underwent a medical in London on Wednesday.
He is expected to become Tottenham’s first signing in 512 days since Lucas Moura joined the club from Paris Saint-Germain.
United are believed to have a sell-on clause inserted into the deal and also first refusal if Spurs decide to loan him back out to continue his development.
Clarke’s exit will intensify the need for Leeds to bring in some new options on the flanks, with Wolves’ winger Helder Costa, Liverpool’s Ryan Kent and former loanee Jack Harrison being active targets, along with Brighton defender Ben White.
Leeds are yet to announce a close-season signing so far this summer.
York-born Clarke made his Whites debut as a second-half substitute in the 1-1 Championship draw at home to Brentford last October.
He netted his first Whites goal to set up a stunning comeback in United’s dramatic 3-2 victory in their televised game at Aston Villa just before Christmas on December 23.
Clarke also found the net in the 4-2 loss at Nottingham Forest on New Year’s Day with his first of four league starts arriving in the 2-0 win at home to Derby County on January 11.
The teenager’s rapid progress was halted when he collapsed on the substitutes’ bench in the draw at Middlesbrough in February with Clarke taken to hospital before being released and returning to training three weeks later.
Sheffield Wednesday are understood to have finalised personal terms with Cardiff City winger Kadeem Harris, who reportedly underwent a medical at the club on Tuesday.
Harris, 26, who had a loan spell earlier in his career at Barnsley, is set to sign a three-year deal and join on a free transfer following the expiration of his Bluebirds’ contract at the end of this month.
Wednesday have also lined up moves for defensive pairing Julian Börner and Moses Odubajo with the announcements expected to be made official once the Owls’ soft embargo is lifted by the EFL – with the club hopeful of satisfying those requirements shortly.