In a statement released by 110Sport, whose football division is headed by Barr's agent Kevin Drinkell, the defender said: "Naturally I am pleased to have sorted out the next stage of my career and glad to end the speculation."
Glasgow-born Barr is "thrilled" over the prospect of joining Hearts but he maintains he is focused on helping Falkirk climb off the bottom of the SPL.
"While I am looking forward to making the move my immediate priority is, as captain of Falkirk, to lead them away from the relegation zone in the SPL," Barr said.
"I have enjoyed my time at Falkirk, and while there was an option for me to leave in this transfer window, I have always stated I was happy to see out the remainder of my contract and the season with the club.
"I want to leave on the best of terms with everyone at the Falkirk Stadium and keeping the club in the top flight will go a long way to guaranteeing that.
"But it goes without saying that I am thrilled with the prospect of joining Hearts, who I believe, will give me the best opportunities going forward."
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Source: Team Talk