The former Newcastle captain was confirmed as the Meadow Lane club's boss on Thursday, and was due to take his first training session on Friday.
Nolan was introduced to the press alongside County's new chairman and owner Alan Hardy, who told his club's official website: "I am absolutely delighted that Kevin has agreed to become our new manager.
"He is a consummate professional with vast footballing experience and I was very impressed with what he has to say when we discussed the vacancy. I thoroughly look forward to working with him."
Nolan - who made 91 appearances for United between 2009 and 2011 - will be reunited with his former Newcastle team-mate Alan Smith, who had been acting as County's caretaker manager.
Nolan previously managed Leyton Orient for a short spell last year.