The England forward has been given the armband by Louis van Gaal, while Darren Fletcher has been named vice captain.
The England international was widely tipped to take over from Nemanja Vidic for the coming season under David Moyes, but the Scot's dismissal led to doubts over who would take the armband.
The club confirmed following the friendly win over Valencia that Rooney is Louis van Gaal's choice to lead the team in 2014-15, with Darren Fletcher named vice captain.
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Rooney said: "It is a huge honor for me — and for my family — to be named captain of this great club. It is a role I will perform with great pride. Team spirit has always been very high in our dressing room and I am very grateful to the manager for the faith he has shown in me. I look forward to leading the team out on Saturday at our first match of the new season."
Darren Fletcher said: "I am delighted to have been named as vice captain. It's a very proud moment for me and my family. Wayne and I have always worked well together and we will continue to work closely together in our new roles. I would like to thank the manager for putting his trust in me."
Van Gaal added: "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."