Duffy, 31, moved to Meadow Lane last summer and made 47 appearances for Kevin Nolan's side.
The central defender scored four goals - his highest tally in a season - as Notts finished 16th in League Two, 10 points above the relegation zone.
Notts have not disclosed the length of the contract for Duffy, who is a former Wales international.
Notts County defender Richard Duffy has agreed a new contract with the League Two side.