Ross Irving, a Conservative and Independent Alliance councillor, said the far right party's national policies were a "total anathema" to him.
Mr Irving defeated City Independent candidate Brian Ward to replace Labour's mayor Mark Meredith.
Councillor Alby Walker, group leader of the BNP, which has nine members on the council, said he "wasn't surprised".
He added: "He is part of the former executive and he's obviously taking instructions from Conservative head office."
Eight BNP councillors boycotted the leader ballot after Councillor Walker came last in the second round.
Mr Irving said: "It's unfortunate that some of their national policies, to people like myself, are total anathema and I would not be able to work with them in an executive capacity."
The council has replaced its unique version of the elected mayor system with a council leader and cabinet set-up following criticism that the city's political system was not working.
The BNP's nine councillors makes it the joint third-largest group on the authority along with the Conservative and Independent Alliance.
The largest group is the City Independents, which has 15 seats, followed by Labour which has 14.