Boss David Moyes had also been hoping to sign a striker, but may now need to pay more attention to central defence, with England international Phil Jagielka out for six weeks with a knee injury and Sylvain Distin suffering a hamstring injury in the 2-0 defeat by Tottenham at White Hart Lane.
Gibson's former manager, Sir Alex Ferguson, is backing the Irishman to do well at Goodison Park.
"I think it's a good move for him," said Ferguson.
"He's got terrific ability, Darron, but he knew he wasn't going to be a first-team regular here all the time.
"He played some terrific games for us but unfortunately he got an injury in the early part of the season that kept him out for 10 weeks but he's fit again and it's a good opportunity for him."
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