The Swede, 24, arrives at Tynecastle Stadium following a successful trial period with the Scottish side.
Sow spent last season with Palace, though he failed to make an appearance for the Premier League club.
"He's a tall, athletic player who will add strength to our forward line," head coach Robbie Neilson told Hearts' official website.
"He's a quality player and spent last season down in the English Premier League with Crystal Palace, so it's a bit of a coup to get him here."
Sow had been linked with a move to Blackpool before finalising his switch to Hearts.