On appointing the England striker as skipper, Van Gaal said: "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."
Speaking to ManUtd.com after watching his side defeat Valencia 2-1 at Old Trafford on Tuesday, the Dutchman added: "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."
The new captain Rooney said: "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."
Scotland international Darren Fletcher has been appointed vice-captain.