Stewart spent this season on loan at Hearts, making four appearances, and will join on a two-year deal once his Livingston contract expires on June 10. He will remain back-up to first-choice keeper Craig Gordon next season.
Hearts intend to sign a number of new faces to strengthen their squad for the top flight, with Savage determined to identify the right candidates in tandem with manager Robbie Neilson.
“I’m delighted to get Ross on board permanently,” Neilson told the club website. “He’s made a big impact in the dressing room since he came in and I know he’s a popular figure.
“Most importantly he’s a good goalkeeper who has improved every week thanks to working with [goalkeeping coach] Paul Gallacher and Craig Gordon.”
Savage added: “We’ve been speaking to Ross for a while and there was an eagerness on both sides to get a deal sorted.
“Sometimes it can be a tough task to get the right personnel for your goalkeeping department but in Ross we’ve got a talented keeper and guy who has just slotted in seamlessly, so this was a straightforward exercise.
“Robbie and I will continue to work hard to ensure that we bring in the right players to this club, players who will help us to make an impact in the Premiership next season."
Stewart is eager to play in front of the Tynecastle Park crowd next term. “I’m really happy to have committed my future to Hearts,” he said. “I’ve enjoyed every minute of my time here so far and I can’t wait to get going again in the Premiership next season.
“The boys have been great since I first came in and it feels like I’ve been here forever. Winning the Championship with this team was a special moment for me and I hope everyone gets to enjoy some more special moments next season.
“It was an honour to play for Hearts this season and I’ll keep working hard in training to make sure I’m ready if the manager calls upon me next season – and hopefully I get to experience playing in front of the fans at Tynecastle as soon as possible.”