The Brazilian full-back joins the Welsh club on a permanent deal, while Zaha has secured a loan switch until the end of the season.
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"My phone is ringing and I am answering most of them. Maybe some players will go out on loan, but we are done with signings," Solskjaer told reporters.
"Some players I have looked at and some have not come through. I can't confirm or deny anybody.
"We have added three new players this week - Fabio, Kenwyne and Wilf. They have energy and enthusiasm and presence - together they complement my squad and I am happy with what I have now."
Zaha joined United in a deal reportedly worth up to £15 million in January 2013 but, after spending the rest of the 2012-13 campaign on loan at former club Crystal Palace, has found first-team opportunities difficult to come by under David Moyes.
Fabio, meanwhile, spent last season on loan at QPR after failing to hold down a place in the United team despite starting the 2011 Champions League final.