The 31-year-old has more than 500 professional appearances to his name for clubs including QPR, Oldham and Leyton Orient.
Forbes joined the Spireites last summer and played the last of his 21 games for the club in a 3-2 League Two defeat to Bristol Rovers in November.
He also started and scored during Chesterfield's resounding 6-1 FA Cup victory over Hartlepool earlier that month and is unavailable for the Shots' weekend trip to Middlesbrough as a result.
Aldershot manager Dean Holdsworth told his club's official website: "Terrell is vastly experienced. He has a good character and is really eager to come and join us.
"He will be a valuable part of our squad."