Elliott has signed a two-year contract with Hearts.
“Stephen’s a player I have known about for a while and is someone who has proven himself to be a goalscorer wherever he has played,” Hearts manager Jim Jefferies told the club’s official website.
“He has an excellent pedigree and has played at the highest level with the Republic of Ireland.
“I am delighted to have brought him here as there was a lot of interest in him from down south.
“He has partnered Kevin Kyle up front before in his Sunderland days so I’m looking forward to seeing the pair link up again.
“I have spoken to a number of people in England about him and they have all given me glowing recommendations. I think he will do really well here.”