Full-back Gibbs was shown a red card in a case of mistaken identity during the first half of Saturday's 6-0 thrashing at Chelsea by referee Andre Marriner, instead of Oxlade-Chamberlain - who had committed the handball in the six-yard box and indeed admitted his guilt at the time, but was waved away.
The FA confirmed on Monday evening the sanction against Gibbs had been removed, and instead transferred onto Oxlade-Chamberlain. However, Arsenal then subsequently moved to have that offence downgraded on appeal, claiming the England midfielder had not in fact technically prevented a clear goalscoring opportunity as the shot from Chelsea's Eden Hazard looked to be going just wide.
That claim was also upheld, meaning both Gibbs and Oxlade-Chamberlain will be able to face Swansea.
A statement from the FA read: "An Independent Regulatory Commission today heard two claims from Arsenal, one of mistaken identity and the other of wrongful dismissal, both in relation to Saturday's game against Chelsea at Stamford Bridge.
"The commission ruled that the dismissal of Kieran Gibbs was a case of mistaken identity and transferred this to his team-mate 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 This claim was upheld, meaning Oxlade-Chamberlain will not serve any suspension with the standard punishment withdrawn with immediate effect."
The heavy defeat on Saturday lunchtime ruined manager Arsene Wenger's 1,000th match in charge and severely dented any Barclays Premier League title ambitions, with the Gunners now down in fourth place, albeit still with a match in hand on the leaders.
Wenger - who cancelled Monday morning's scheduled pre-match press conference - has been left puzzled by his side once again failing to turn up in a big game; Arsenal found themselves 3-0 down by 17 minutes, and played out the rest of the match with 10 men after Gibbs' sending off.
Midfielder Mikel Arteta has issued a public apology on behalf of the Arsenal players for the "unacceptable" and "embarrassing" humiliation - and vowed they will get things right against Swansea.
Arteta accepts the Gunners were "just not good enough" and have no option but to raise performance levels against the Swans, with the squad having held a debrief session at their London Colney training base on Sunday.
"We paid for our own mistakes. We have to take it on the chin because it is unacceptable to lose another big game like this," the Spaniard said to Arsenal Media.
"You cannot only just move on, you have to analyse what you have done and react. I am expecting a big reaction on Tuesday (because) Saturday was not good enough for this football club.
"The good thing is we have a lot of things to play for and we have always reacted to disappointments and difficult moments, but this one is a really hard one to take, it was a massive game for us and for me it is unacceptable.
"The pressure we put on ourselves by losing games like that is massive and there is no need for it.
"We just disrupted the good season we were having. I don't know what else to say apart from sorry to everyone at the club, the fans, and we promise that we will try hard to put that right."
Arteta stressed none of the players wanted to produce another shocking display like they did at Stamford Bridge - which had followed on from heavy defeats at both Manchester City and Liverpool earlier in the season.
"It hurts deeply inside. It is embarrassing to be on a football pitch in that situation," he said.
"Psychologically it is really hard, and when you go through that you analyse it and you know you don't want to be in that situation again.
"I promise everyone that we have that hunger to put it right. On Tuesday, we have an opportunity again at home and we just need to bounce back."
Arsenal will be without defender Laurent Koscielny because of a calf problem.
Captain Thomas Vermaelen is likely to play at centre-half alongside Per Mertesacker, while 19-year-old Spaniard Hector Bellerin, who was on loan at Watford, has been drafted into the squad as cover.
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