Sissoko's stock sky-rocketed following an impressive European Championship display with France and a man-of-the-match performance in the final defeat by Portugal.
He had not made an appearance for Newcastle in the Championship this season as the club sought to ship him out to the highest bidder.
Spurs have matched their club transfer record by signing Sissoko, rivaling the £30m Tottenham paid Roma for Erik Lamela in 2013.
As the clock ticked down towards the 11pm deadline, tension was building in North London and on Tyneside as both Newcastle and Spurs sought to tie down a deal.
It was a day of typical Daniel Levy drama, as the Spurs Chairman left it late to secure his manager's target.