The long-serving all-rounder will succeed Chris Read, who retired from first-class cricket this year.
Mullaney, 31 on Sunday, will serve as skipper in four-day and 50-over cricket, with a decision to be made at a later date on the T20 captaincy.
The appointment was recommended by director of cricket Mick Newell and head coach Peter Moores and approved at a meeting of the club’s general committee.
“It’s a huge honour and a privilege to be asked to be captain of such a great club as Nottinghamshire, and one that has such a long and proud history and tradition,” said Mullaney.
“It’s an illustrious list of names that I am following in the footsteps of. Hopefully I can live up to the expectation of being Nottinghamshire captain and can deliver more trophies.
“It’s something I will give all of my energy to. If I can do half the job that my predecessor Chris Read has done for this club in the last 10 years, then I’ll be a happy man.”
Mullaney’s elevation to captain comes after two impressive seasons at Trent Bridge that have been among his best since first joining the club from Lancashire for the start of the 2010 season.