Zaha was in the England squad at the beginning of last season but made only four appearances for United before being loaned to Cardiff City.
Zaha said: "It's great to be back. There's a nice vibe, everybody's working hard and we're looking forward to the new season.
"For me, I definitely feel like this is a clean slate.
"All I'm trying to do is impress the new manager and get into his squad.
"All I can do is give my all. There's a new manager and I want to make sure I show him what I can do."
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