Rose was given a straight red for a tackle on Dzeko inside the home penalty box during Tottenham's 5-1 defeat to Manchester City at White Hart Lane on Wednesday.
Replays showed Rose clearly made contact with the ball, but a penalty was awarded by referee Andre Marriner after his assistant Scott Ledger flagged for a foul.
After studying replays of the incident, which happened when City were 1-0 up, the FA has decided to rescind the red card.
That means Rose will be available to play in Spurs' away game at Hull on Saturday.
An FA statement read: "Danny Rose's one-match suspension has been withdrawn with immediate effect after the Tottenham player's wrongful dismissal claim was upheld by an Independent Regulatory Commission.
"Rose was dismissed in Tottenham's game against Manchester City on Wednesday for denying a goalscoring opportunity."
Spurs boss Tim Sherwood said immediately after the match that the club would appeal, adding: "I think Andre got it right in the first place when he called it as a corner.
''Unfortunately for us, the linesman decided that Andre got it wrong and he's given a penalty there. I think Danny's making a last-ditch tackle so he's having to lunge in there a bit. He clearly wins the ball."