The FA accused Arsenal fans of provoking Adebayor after giving the City striker a two-match suspended ban and £25,000 fine.
Adebayor is now available for City's Barclays Premier League trip to Aston Villa on Monday as the ban will only be triggered for a similar breach of FA rules before December 2010. And Hughes admitted he was delighted with the news that he will have his leading scorer back in action.
"There has been a lot said and written about Emmanuel's goal celebration," Hughes said. "We are just glad to put it all behind us now and I am relieved he will be able to play at Aston Villa on Monday night.
"Manu was in great form before his suspension and having him available again is a huge boost to us.''
The 25-year-old has already served a three-match suspension for violent conduct in a separate incident during the victory at Eastlands last month, although there was the possibility of further action after he sprinted the length of the pitch to celebrate in front of visiting fans following his headed goal.
It is understood the Togo striker was at Wembley to admit a charge of improper conduct to an FA regulatory commission hearing. His admission was taken into account as was, crucially, the conduct of Arsenal fans.
"In reaching its decision the commission took into account his admission of the charge, public apology and the extremely provocative nature of the abuse he received,'' read an FA statement.
"However, the commission also stated that players have a responsibility to conduct themselves in a proper manner and that such celebrations are unacceptable and have the potential to cause a serious public order incident.''
Arsenal fans have been criticised for personal abuse of Adebayor after he left them in the summer. He felt he was a scapegoat for supporters during his final days at the Emirates Stadium.
City were expected to use the evidence of Gary Neville's goal celebration against them the following week - which did not even bring a charge against the Manchester United defender - as part of their defence.