The 22-year-old had been frozen out of Hearts' first-team squad since the arrival of new boss Csaba Laszlo and is desperate to move on.
Livingston Chairman Angelo Massone told the club's official website: "We are delighted to have reached an agreement with Hearts, and very pleased that a player of Calum Elliot's quality is coming to the club.
"I am certain that he will prove a valuable addition to our pool of players."