The 21-year-old, released from Upton Park at the end of last season, is the second ex-Hammer to arrive at Brisbane Road on Friday after Blair Turgott signed on the dotted line.
McCallum, who has had loan spells at AFC Wimbledon, Aldershot, Torquay, Hearts and Portsmouth, has agreed a two-year contract.
Hendon told the club website: “Paul is a big, lean striker who is willing to work as a centre-forward.
“He will go and shut down and do the other side of the game. When it goes up he will get hold of it and bring others into play. He is proven at this level when he has been out on loan.”