The 28-year-old England striker succeeds Nemanja Vidic after the Serbia defender left United at the end of last season to join Inter Milan.
"For me it's the choice of captain is always very important," said Van Gaal in a club statement issued after United's 2-1 friendly win against Valencia at Old Trafford yesterday.
"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," the Dutchman explained.
Rooney, who could now also become captain of England following Steven Gerrard's retirement from international football, said, "It is a huge honour for me -- and for my family -- to be named captain of this great club.
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"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."
"I am delighted to have been named as vice-captain," Fletcher said. "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 was appointed after United, who finished a relatively lowly seventh in the Premier League last term, sacked David Moyes -- retired manager Alex Ferguson's chosen successor -- after the former Everton boss failed to complete his first season in charge at Old Trafford.