The North-West outfit confirmed the appointment of the Netherlands boss on a three-year deal on Monday.
Despite United falling from first to seventh in the Premier League table under Moyes, Keane believes that the Scotsman deserved more time to get things right at Old Trafford.
"I thought David Moyes was a good choice and I felt he maybe should have got a bit more time," The Independent quotes Keane as saying.
"Van Gaal is obviously a vastly experienced manager. He has worked at big clubs, Bayern [Munich], Barcelona, he's been involved with national teams before, so fingers crossed he'll come in and do the business."
Van Gaal will take on the United role after the World Cup in Brazil this summer.