Van Gaal made the announcement following United’s final pre-season friendly against Valencia, when Rooney skippered the side to a 2-1 victory courtesy of Marouane Fellaini’s late goal.
The England international, who is also in the running to skipper the national side in the wake of Steven Gerrard’s international retirement, takes over the role from Nemanja Vidic, who departed for Inter Milan in the summer.
Midfielder Darren Fletcher has been named as the club’s vice-captain after Van Gaal handed a number of different players the armband in pre-season.
Rooney told the club’s official website: "It is a huge honour 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."
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."
And 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."