Stepney has tipped the 20-year-old goalkeeper to be a real success at Old Trafford.
United announced on Wednesday the signing of De Gea on a five-year contract from Atletico Madrid.
“He’s done very well for Atletico,” Stepney told United’s official website. “His record last season (24 clean sheets in 45 games) is incredible in a top-class league. I’ve only seen him on TV and you can’t tell everything about a player on TV.
“For example, I always like to see what a goalkeeper’s doing position-wise when the ball’s down the other end of the pitch and the cameras rarely show that. But certainly I’ve seen what a good shot-stopper he is and it would seem that he’s going to be Sir Alex’s number one.
“We’ve also still got Anders Lindegaard, Ben Amos and Tomasz Kuszczak on the books, of course, and one of them will have to leave, either on loan or permanently. A club like Manchester United has to have three top-class goalkeepers because if your number one gets injured, you need quality cover in the team and on the bench.”