The Crystal Palace forward has agreed personal terms and will undertake a medical in Manchester today (Friday 25 January).
Crystal Palace's official website report the deal should be concluded early next week, with Zaha loaned back to the Eagles until the end of the season. He will join his new United team-mates in July 2013.
“I'm delighted to be joining Manchester United and ending the recent speculation," the 20-year-old said.
"I would like to thank the owners at Palace for making the move possible, however my focus for the next five months will be solely at Crystal Palace.
"I have been at Palace for more than 10 years, I will always love the club and I want to help get them back to the Premier League, particularly for the fans who have always been so good to me.”