McCallum, 20, has spent loan spells at Rochdale, AFC Wimbledon, Aldershot and most recently at Torquay United.
He will training with his new team-mates on Friday and is line to feature in Sunday's League Cup semi-final against Inverness CT.
Hearts manager Gary Locke told the club website: "Paul comes highly recommended.
"He has a good pedigree, is powerful, good in the air and can score goals.
"I am sure he will be a good asset to the squad and he gives us an extra option, and is something different to what we have here.
"Hopefully he does well for us and can hit the ground running."
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