The Dutchman told the club's official website: "For me it's always very important the choice of captain. Wayne has shown a great attitude towards everything he does.
"I have been very impressed by his professionalism and his attitude to training and to my philosophy. He is a great inspiration to the younger members of the team and I believe he will put his heart and soul into his captaincy role.
"Darren Fletcher will become the vice-captain. Darren is a natural leader and will captain the team when Wayne isn't playing. Darren is a very experienced player and a very popular member of the dressing room, I know he will work well alongside Wayne."
England forward Rooney has also been tipped to inherit the armband at international level following the retirement of Steven Gerrard.
Th 28-year-old is United's third leading goalscorer of all time, behind Sir Bobby Charlton and Denis Law, having netted 216 goals in 442 games since joining the Red Devils from Everton as a teenager in 2004.