The Dutchman was confirmed as David Moyes's successor on Monday, signing a three-year contract.
Should Moyes have stayed, Rooney was expected to be named permanent captain for next season, but he is now facing the prospect of playing second fiddle to Van Gaal's current Netherlands skipper Robin van Persie at Old Trafford.
However, Rooney has still declared that he is "looking forward" to working with the Dutchman.
He tweeted: "Great to see Louis Van Gaal has been named @ManUtd manager. Looking forward to working with him."
Van Gaal has previously managed Ajax, Bayern Munich and Barcelona to domestic championships.