Paul Chambers, a 27-year-old from Doncaster who now lives in Northern Ireland, was convicted in May 2011 of sending a "menacing electronic communication" on Twitter.
After Robin Hood Airport in South Yorkshire was closed following heavy snow, Chambers tweeted to his 600 followers: "Crap! Robin Hood airport is closed. You've got a week and a bit to get your s**t together otherwise I'm blowing the airport sky high!!"
After being found guilty at Doncaster Magistrates Court last year, an initial appeal was dismissed, leading Chambers's legal team to escalate the challenge to the High Court.
Today, the conviction was quashed after Chambers's legal team successfully argued that he sent the tweet in January 2010 in a moment of frustration, and never thought anyone would take his "silly joke" seriously.
In their verdict, Justice Owen and Justice Griffith Williams said there had been no evidence that any of Chambers's followers had found his tweet to be "of a menacing character or, at a time when the threat of terrorism is real, even minimally alarming".
"In fact nothing was done about it by anyone until January 11, 2010, some five days later when the duty manager responsible for security at Robin Hood Airport, while off duty at home, found it," said the judges.
"Mr Duffield did not see this tweet on the appellant's time line, and it was never sent to him or to the airport. Rather he was at home searching generally for any tweets which referred to Robin Hood Airport."
The judges noted that security officials at the airport had labelled the threat from the tweet "non credible", as it was displayed alongside Chambers' name and it was clear that he intended to use the airport again the future.
In concluding, the judges said: "The appeal against conviction will be allowed on the basis that this tweet did not constitute or include a message of a menacing character; we cannot usefully take this aspect of the appeal further. "
Following the verdict, IT Crowd creator Graham Linehan, who has campaigned on behalf of Chambers, tweeted: "Just amazing. Can't believe it. What great news."