McCallum has spent much of this season on loan at the Shots' npower League Two rivals AFC Wimbledon, scoring four goals in nine appearances for the Dons.
Aldershot manager Andy Scott told the club's official website: "I am delighted to welcome Paul to the club.
"I have watched him on many occasions for West Ham's Under-21 team and he impressed. He also did well on loan at AFC Wimbledon earlier this season." .
"Paul is keen to do well and wants to score the goals which will help the club preserve its Football League status."
McCallum joined West Ham in January 2011 after rising through the ranks at non-league Dulwich Hamlet.
The 19-year-old, who recently signed a new two-and-a-half-year deal with the Hammers, is expected to make Aldershot's trip to Bradford on Saturday.
- Sports & Recreation
- AFC Wimbledon