The 33-year-old, who has penned a one-year contract, will act as a player-coach at the League One club.
Smith had spent the past two years at MK Dons, but a failure to agree a new deal has seen him move on.
"I am absolutely delighted," County boss Shaun Derry told BBC Sport. "Everyone is aware of what he is as a player and where he has been and the fantastic clubs he has been at.
"But he is not just joining to be a player who can produce the performances, he will be a fantastic influence in the dressing room - which is where I felt we struggled."
Smith started his career with Leeds United before spells with Manchester United, Newcastle United and MK Dons.
He also scored one goal in 19 appearances for England during an international career that lasted from 2001 to 2007.