The 23-year-old stand-off qualifies for Scotland through his grandparents and will team up with Mike Blair’s squad in the summer at the end of his current deal.
Healy, who has played for Ireland Under-20s, said: “Edinburgh is a hugely welcoming club with a really tightknit playing squad.
“It’s also been great to see the club move into a new home in DAM Health Stadium which looks to have a brilliant atmosphere.
“Having played against them several times it’s clear how much they want to play. They’ve really developed their game under Mike and I believe that style will suit me.
“I’m looking forward to putting myself into a new environment and seeing how I go.
“I’d like to thank everyone at Munster for their support over the last few seasons. I’ve loved every minute of my time playing with the club, but I felt now was the right time to take on a new and exciting challenge in Edinburgh.”
Edinburgh head coach Blair believes the player will be a big asset in his squad, with Glasgow Warriors having failed in a bid to land the player a few years ago.
He said: “We’re absolutely delighted to secure Ben’s signature. He’s a quality playmaker who brings excellent game management and kicking ability to our already talented group of 10s.
“He’s kicking at goal at over 90 per cent accuracy so far this season while his performances – from both the bench and in starts for Munster – have been hugely impressive.
“He’s got great calmness around the way he dictates play and influences matches.
“With Ben being Scottish qualified, that was another important factor in the decision to bring him in, and I know he’ll be really excited to hit the ground running at a new club, and in a new city, while competing for a place in our squad.
“All of us at the club are looking forward to welcoming Ben to Edinburgh this coming summer.”