The 35-year-old has agreed to join the Spireites until January but hasn't ruled out prolonging his stay.
The Portuguese revealed that the move came about after a chance meeting with former Cottagers teammate Mark Crossley, who is now an assistant coach with the League Two side.
"He asked me if I'd fancy coming up to Chesterfield and it went from there," Boa Morte told the club's official website.
"The most important thing for me now is to play football and get going again. I'll be here until the end of January but that doesn't mean that I won't stay until the end of the season."
Boa Morte won the double with Arsenal in 1998 before spells with Southampton, Fulham and West Ham United.