The 27-year-old was made available by Robins boss Paul Buckle last week having fallen out of favour at Whaddon Road.
He joined Cheltenham in January 2013, making 63 starts and 11 substitute appearances, scoring three goals. His final outing for the club was the 1-0 FA Cup first round home defeat by Dover Athletic on December 7.
Taylor passed a medical at Sixfields on Thursday afternoon and will go straight into the Cobblers' squad for their home match against Southend United on Saturday.