The Edinburgh club are understood to have paid a six-figure sum for the energetic 25-year-old in order to reinforce their midfield.
He replaces Olly Lee in the first-team squad at Riccarton after helping Shamrock to the League of Ireland title last year and earning a Republic of Ireland call-up in November.
Hearts’ sporting director Joe Savage explained to the club website that he had been chasing McEneff for some time.
“Aaron is someone that I’ve been looking at for the best part of four years and I’m delighted that we’ve been able to bring him to Hearts,” said Savage.
“He’s been one of Ireland’s standout players for a couple of years now, evidenced by his recent international call up.
“I’m sure the fans are going to be excited by him; he’s really energetic, a box-to-box midfielder who can chip in with goals as well.”
McEneff was on Tottenham Hotspur’s books as a youth player but joined Derry City in 2015 before moving on to Rovers in 2019.
He scored seven goals in last season’s title-winning campaign and hopes to bring his goalscoring form to Scotland.
“Hearts is a massive club and I see it as a massive opportunity to come here and play in Scotland,” he told the club website.
“It’s a new challenge, it’s one that I’m really looking forward to. I know the boys have been doing well this season and I’ll work hard and try and be a part of what’s ahead.
“I would say I’m a box-to-box midfielder, simple as that really. I get into the box and score goals, and when you have to defend you go and do your bit and defend. That sums me up really.
“The manager sees me as a box-to-box midfielder and he wants me to go and get on the end of things in the box and score goals, and be that all-round midfielder that has a lot of energy within the team.
“That suits me because that’s my game. Hopefully I can get going, hit the ground running and show people that I can do that.”