Their clubs appealed after red cards were shown during Everton's 2-1 Premier League win at Upton Park last weekend. Gibson is now available to face Chelsea on Sunday but is unlikely to play after picking up a thigh strain against Wigan on St Stephen's Day.
No action has been taken against Anthony Taylor, the referee who sent the pair off for what he perceived to be dangerous, high tackles. Taylor is scheduled to officiate the Queens Park Rangers versus Liverpool match this weekend.
An FA statement read: " The FA can confirm that red cards shown to both Carlton Cole and Darron Gibson have been rescinded. Their three-match suspensions have been withdrawn immediately and written reasons will be provided at a later date."
The pair became the latest beneficiaries of the rewritten rule on rescinding red cards, which came into force over the summer. Before, red cards were only cancelled if it could be proved that there was a "serious and obvious error". Fifa permitted the FA to change the grounds for rescinding a red card to just an "obvious error".
Sam Allardyce, the West Ham manager, welcomed the decision. "I am delighted that we have got a bit of justice," he said.
The FA has confirmed their comments are "both under consideration" given the edict to managers to refrain from openly criticising the professional standards of referees.
Redknapp was forthright in his criticism of Chris Foy, suggesting he "should have gone to Specsavers" after his performance in West Brom's 2-1 win against QPR at Loftus Road.
"Once a year I might have the hump with a referee, I never knock on their door but that was poor, two vital decisions went against us," Redknapp said.
Both managers' statements are being assessed. (© Daily Telegraph, London)