Sow, who was linked with capital rivals Hibernian at the end of last season, has signed a two-year deal following a successful trial spell.
The 24-year-old Swede spent last term with Crystal Palace but found his chances of a first-team breakthrough hampered by a knee ligament injury. "I'm happy to have signed for Hearts," said Sow. "It's a massive club which should be in the top flight.
"It's a big thing to play in front of so many fans and I've heard a lot of good things about the supporters here.
"If we work hard then we can get some good results, and if I work hard I'm hopeful I'll score a lot of goals here."