District Judge Jonathan Bennett said the message "was of a menacing nature in the context of the times in which we live." He ordered Chambers to pay 1,000 pounds ($1,500) in a fine and costs.
Chambers was arrested in January after he posted a message on Twitter saying he would blow Robin Hood Airport near the large town of Doncaster "sky high" if his flight was delayed.
Chambers, from Doncaster, said he made the post when the airport was closed by snow and he feared his travel plans would be disrupted.
"It did not cross my mind that Robin Hood would ever look at Twitter or take it seriously because it was innocuous hyperbole," he said.
An airport employee came across the tweet a few days later, but security staff there decided it was not a credible bomb threat. They passed the message on to police.
Chambers, who lost his job at a car distribution firm after his arrest, said he was considering an appeal.