The former England and Manchester United midfielder signed a one-year deal to become a player-coach at Meadow Lane on Tuesday.
Smith now hopes that he can help Derry to create a winning mentality among the squad for next season.
"We seem to get on as people," the 33-year-old told BBC Sport. "We are both very honest. We are both very passionate and committed to what we do, and when the opportunity came I jumped at the chance.
"We are trying to create an environment that breeds a winning mentality."
Smith has joined County after failing to agree a new contract with MK Dons.