Leeds, the League One leaders, scored the biggest Cup upset for years when they beat United 1-0.
NEWS: Leeds stun United at Old Trafford
Holders Chelsea, who beat Watford 5-0 on Sunday, will play another Championship side when they travel to Preston North End - their first visit to Deepdale for 29 years. Preston crushed Colchester United 7-0 in the third round.
Arsenal, who scored two late goals to beat West Ham United 2-1 at Upton Park on Sunday, were handed another tricky away tie at Premier League Stoke City, who saw off non-League York City 3-1 on Saturday.
Burnley will visit Liverpool if Rafa Benitez's men win their replay against Reading at Anfield, while Sunderland will face Portsmouth if Pompey win a replay at Coventry City.
Grayson told Sky Sports: "It's another fantastic draw for us, against another top Premier League club and a fixture that would have been a Premier League game a few years ago. We are looking forward to it."
The Yorkshire club have only beaten Spurs once in the competition - in 1972 the year of their only FA Cup success.
Tottenham's former Leeds players Aaron Lennon, Robbie Keane and Jonathan Woodgate will be relishing their old club's visit.
