The 20-year-old winger will cost United £10m up front - the biggest initial payment for a Championship player ever, higher even than the £6m paid for Southampton's Theo Walcott by Arsenal in 2006.
The rest of the transfer fee is dependent on performances and appearances - £3m based on Manchester United appearances, and the remaining £2m dependent on trophies and England caps.
The Daily Mail reports Palace have also inserted a 10 per cent sell-on fee. Zaha is expected to travel to Manchester for a medical within the next 48 hours, and will be loaned back to the south London club for the rest of the season.
The Championship side are well-placed for a promotion push, and the loan-back agreement was thought to be a key stipulation in negotiations.
Zaha, who received his first England cap against Sweden last year, will sign a five-and-a-half year contract with United, on a reported £35,000-a-week.
The news of a breakthrough in the negotiations for Zaha comes at a good time for Sir Alex Ferguson - as recent bad news on the injury front revealed United winger Ashley Young is set to miss the club's Champions League last-16 tie against Real Madrid with a knee problem.
The report claims Young will miss both matches against the La Liga champions, and faces up to four weeks on the sidelines with a damaged left medial ligament.
The England international picked up the injury after a tackle by Daniel Agger during United's 2-1 victory over Liverpool at Old Trafford on January 13.