Sir Alex Ferguson's last signing before his retirement, Zaha joined United in a £15 million deal from Crystal Palace in January 2013 and was immediately loaned back to the Eagles, helping them secure their promotion to the Premier League.
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"It's great to be back," Zaha told United'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."
United will play LA Galaxy, Roma, Inter and Real Madrid during their tour and Zaha is confident he will be given a chance to show his talent as Van Gaal evaluates United's squad ahead of the 2014-15 season.
"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 on 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."