Ole Gunnar Solskjaer had already boosted his squad with the addition of Fabio, Kenwyne Jones, Magnus Wolff Eikrem, Mats Moller Daehli and Jo Inge Berget since succeeding Malky Mackay as Bluebirds boss.
Zaha, 21, is the most high profile of his acquisitions, although it was expected he would choose Newcastle to relegation threatened Cardiff.
Solskjaer said: "That signing should be done by now. His name is on the paperwork. He is a Cardiff player.
"He has pace, power, technical ability and goes past people. He will give us that extra change of tempo in the final third, where we really need it.
"He will bring that little final bit to find pockets of space and produce a bit of magic.
"I don't think he has something to prove, he wants to play," said the former Red Devils striker.
"He played a few games at United, but maybe not what he hoped for when he went there.
"He wants to play, to play with confidence and keep Cardiff in the Premier League."