The 28-year-old was restricted to 18 Bantams appearances after joining last summer because of a broken leg.
Anderson has played 292 times in his career for teams including Nottingham Forest and Ipswich Town.
"Paul is a player of proven quality with a lot of Championship experience," said Cobblers manager Rob Page.
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Northampton Town have signed midfielder Paul Anderson on a one-year deal after he left League One rivals Bradford City by mutual consent.