Gomis has agreed a three-year contract at Tynecastle and will link up again with Craig Levein, who signed him for Dundee Utd, the club where he recently completed a second spell.
The Senegal international's first spell at Tannadice was between 2007-11, ended when he moved to Birmingham City.
After two seasons with Birmingham he returned to United in 2013.
Hearts are also reported to be interested in signing midfielder Prince Buaben, who had a recent spell with Partick Thistle.
Buaben is also available on a free transfer.