Gibbs was sent off for handball against Chelsea on Saturday - an offense actually committed by his teammate - and the Gunners have successfully appealed the red card because of mistaken identity.
Oxlade-Chamberlain, meanwhile, escapes punishment despite being the true culprit because Eden Hazard's strike was sailing wide of the far post.
"The commission ruled that the dismissal of Kieran Gibbs was a case of mistaken identity and transferred this to his teammate Alex Oxlade-Chamberlain.
"Subsequent to deciding this matter, the commission then considered Arsenal’s claim for wrongful dismissal in relation to Oxlade-Chamberlain. This claim was upheld, meaning Oxlade-Chamberlain will not serve any suspension with the standard punishment withdrawn with immediate effect."
Manager Arsene Wenger, speaking ahead of Tuesday's encounter with Swansea, anticipated that both players would escape punishment.
"The sending off is simple," said the Frenchman. "If the red card is rescinded we will have Chamberlain available.
"I believe there are two situations. First, mistaken identity so Gibbs will normally be available, which is the minimum you can expect. After that the second decision depends on whether Chamberlain deserves a red card or not. There the rules are quite clear. If the ball will go in the back of the net it is a red card. If the ball will miss the target it is not a red card, so I believe that this red card will go as well and Chamberlain will be available."
Referee Andre Marriner has escaped demotion despite the blunder and will take charge of Southampton against Newcastle at the weekend.