David Moyes has allowed Fabio, who has been with the Reds since 2008, to join Ole Gunnar Solskjaer's side for an undisclosed fee after being unable to guarantee him regular football at Old Trafford.
The Brazilian defender told Cardiff's official website: "I’m very excited to be part of this and I’m looking forward to helping Cardiff.
"I know this is the right move for me. I spoke a lot to the manager about coming in and I know that I can help us move up the division."
Zaha, meanwhile, will play for the Bluebirds for the rest of the season and Moyes hopes the winger's temporary move will benefit United next term.
"I said right at the start of the season that if I could get Wilf the games, I'd keep him, but if I couldn't then I’d get him some games on loan," Moyes said.
"There were a few clubs who wanted him on loan but in the end we felt Cardiff was the right choice for him. Hopefully he will go and get those games, show what he can do in the Premier League and be ready to come back to us at the end of the season.