The 28-year-old, who spent a loan period at the club earlier in the season, was a free agent having departed Chesterfield by mutual consent earlier in the month.
According to the Express and Star, the current deal will expire at the end of the campaign, but there is the option of a further one-year contact.
"I'm really looking forward to the challenge. Since the very first day I arrived here, this club has always been a perfect fit for me and I believe that I can really progress here," Westcarr told reporters.
Westcarr started his career at Nottingham Forest.