De Gea admitted Atletico had fought to keep him at the Vicente Calderon but felt the time was right to move on.
"Atletico Madrid made an offer to renew my contract in September or October and I said that I wouldn't study it until the Under-21 European Championships finished and do it with a little more calm," said De Gea.
"In these cases it's important that your family advise you and they've done that.
"Atletico have always fought for me. I've always felt wanted, but the main reason for my going is that I want to play at Manchester (United).
"Manchester United are one of the best clubs in the world and it's an important step in my career. I'm going to do as well as possible there and try to succeed."