The Scottish Premiership side announced the news on the club's website on Wednesday.
McKenna, 21, was a mainstay in Ray McKinnon's team after joining the club in January from the US where he did a scholarship at Duke University in North Carolina and played for the Blue Devils and Jacksonville Armada.
The former Celtic youth academy player made 17 appearances for Falkirk, scoring twice but was unable to save the Bairns from relegation to League One.
Accies chairman, Allan Maitland said: "Ciaran is a great talent and we’re delighted to have the deal over the line."
McKenna becomes the 16th player to leave Falkirk since the end of the season.