The 20-year-old donned the number one shirt at Old Trafford after the veteran Dutch goalkeeper retired at the end of last season.
"They scouted all over Europe and found a couple of targets and they chose De Gea," Van der Sar told ESPN Star. "Hopefully he's going to have a great career at Manchester United.
“He's very talented. He's already won a trophy with Atletico Madrid and the Spain Under-21 team, so the prospect of him doing well is there.
"Everybody has to be his own person. I've met him and it looks to me as though he can handle it."
The Spaniard was Sir Alex Ferguson’s third signing of the summer, following Phil Jones and Ashley Young.