The Toffees have moved to replace Marouane Fellaini, who has joined Manchester United in a £27.5 million deal, with both the Wigan youngster and the 32-year-old Man City loanee
Everton have completed the signing of Wigan midfielder James McCarthy for £13 million, as well as addingManchester City veteran Gareth Barry on a season-long loan deal.
The Toffees have had a busy transfer deadline day, bringing in three new faces - McCarthy, Barry and Chelsea loanee Romelu Lukaku - while offloading Marouane Fellaini and Victor Anichebe.
"Roberto Martinez moved to boost his midfield by signing James McCarthy from his own former club Wigan Athletic," read a statement on the club's official website.
"The highly-rated 22-year-old arrives with an impressive reputation as one of the game's brightest young talents."
Wigan owner Dave Whelan had earlier blasted Everton's initial bid for the Republic of Ireland international, but revealed that the two clubs had eventually reached an agreement over the pay structure of the deal.
"They've been realistic and have matched our valuation. They are going to pay us much, much quicker than they said they would earlier," he told BBC Radio 5 Live.
"It's now up to them and they have to try and get it through. If he goes, he goes, and we wish him all the best, if it doesn't go through then I hope he'll play as normal for Wigan."
Barry, meanwhile, has joined on a temporary basis after finding first-team opportunities hard to come by at the Etihad Stadium.
"The final piece of the deadline day jigsaw sees England international and Premier League and FA Cup winner Gareth Barry arrive from Manchester City.
"The 32-year-old brings a wealth of experience to the Everton midfield having also played for Aston Villa in the Premier League."