The 22-year-old has been at the club for 14 years but will be searching for a new club this summer.
The winger spent the second half of the season on loan at Arbroath where he impressed across his eight appearances.
Moore revealed he would be departing Tynecastle on Twitter.
“After 14 years, my time at @JamTarts is finally up at the end of the month," he posted.
"I’ve made memories I’ll never forget and friends for life. Thanks to everyone for the support over the years! It’s been a pleasure.”
Moore made 26 appearances for Hearts and also had loan spells at Cowdenbeath, Falkirk and Forfar Athletic during his time at the club.