Zaha was signed for £15million by former United manager Sir Alex Ferguson but struggled to impress his successor David Moyes and was farmed out on loan to Cardiff last season.
The 21-year-old gained valuable Premier League experience as he made 13 appearances for the Bluebirds and he is keen to show he has grown as a player during his time away from Old Trafford.
"It's great to be back," Zaha told the club's official website. "There's a nice vibe, everybody's working hard and we're looking forward to the new season.
"Going to Cardiff was a really good experience for me. I managed to get quite a few games under my belt at Premier League level, which was good, and I feel like I've come back a better player.
"I've realised there are things about my game I need to work on and concentrate on and I know this is the best place to be if I want to improve. I really want to make myself a better player."
Zaha shone on United's pre-season tour of Australia last season but struggled to get playing time during the campaign, making just two starts and two substitute appearances before leaving for Cardiff in January.
The winger is one of a large group of players who are keen to impress van Gaal after a below-par season at Old Trafford which saw United limp to a seventh place finish in the league.
United's new manager has said he will spend a couple of weeks closely observing his players before deciding what positions need strengthening and who will be allowed to leave.
Zaha is determined to impress the Dutchman and ensure he will have a future at Old Trafford.
"For me, I definitely feel like this is a clean slate," Zaha said. "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.
"United are a big club so we need strong opposition and we've got that in pre-season this year.
"There's no doubt we'll be tested on tour and that's a good thing. It should prepare us well for the season ahead. I'm really looking forward to being involved and I can't wait to face those teams."