The 22-year-old twice-capped England international is thought to have agreed a five-and-a-half year contract with the London club.
Zaha moved from Selhurst Park to Old Trafford in 2013 but his career with the then Premier League champions failed to ignite as he made just four appearances in all competitions before joining Cardiff City on loan last January.
An initial return to Palace on loan in August and, following 19 outings and one goal this term, manager Alan Pardew has moved to make Zaha's stay a long-term one.
"Glad to be back permanently and appreciate all the messages," Zaha said on his Twitter account.
Crystal Palace are currently 13th in the Premier League, four points above the relegation zone.
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