The 32-year-old has been looking for a new club since his release from First Division side Sheffield United at the end of last season and spent time training with the Sixfield Stadium outfit before signing.
The former Norwich City, Osasuna and Leicester City man has already appeared in The Cobblers' reserves and he will be available for Northampton's trip to Scunthorpe United on Saturday.
Meanwhile, Calderwood has terminated the contracts of three midfielders in Aaron Cavill, Dean Cracknell and Paul Rickers.
The trio have failed to make much of an impact with The Cobblers and the former Tottenham Hotspur coach has decided to let the players move on.
"I would like to thank all three players for their efforts here," Calderwood told the club's website.
"Everyone at the club would like to wish them every success for the future."
