The 22-year-old, who scored 43 goals in 81 appearances for the Championship side after joining them as a trainee in the summer of 2010, has signed a three-year deal.
Hearts have agreed compensation with Queen of the South for a development fee for the player who was out of contract at Palmerston Park.
Speaking to Sky Sports News HQ, Reilly, who scored 15 goals in 39 league games last season, said: “It’s great to sign here and I am glad it’s finally done and dusted as this is a great club to be at.
“The manager has told me I bring something different to what he already has here. I have pace, energy and I work really hard so hopefully I can bring these into the Hearts squad and benefit them.
“I played against Hearts four times last year and they are a really great squad and they deserved to win the league in the manner they did.
“Everyone says their aim next season should be top six but I feel this team can go further than that. To begin with that may be our target but who knows. They are a really, really great squad.
“This is a big step up for me but it’s what I have been aiming to do for the last few years so hopefully I can stamp my authority on the Premiership and hopefully score some more goals at this level.”
Reilly becomes manager Robbie Neilson’s second acquisition of the summer as he prepares his side for a return to the top flight of Scottish football.
Earlier this month, Polish defender Blazej Augustynl, who started his career in England with Bolton Wanderers, agreed a switch from Gornik Zabrze, subject to international clearance.
And Neilson could be set to further boost his squad as Sky sources understand 24-year-old Spanish striker Juanma, who plays for Greek side Kalloni, could arrive at Tynecastle in the next few days.
Hearts begin life in the Premiership at home to St Johnstone on Saturday, August 1. Click here for their season’s fixtures in full.