Toffees boss David Moyes has fended off strong competition from a number of clubs all over Europe to land the Dutch international.
The 22-year-old, who started his career at Feyenoord before joining Twente in 2011, will move to Goodison Park once personal terms have been agreed and a medical been passed.
Fer, nicknamed 'The Bouncer' due to his physical strength, hit headlines last year when he spent £22,000 on a horse for his girlfriend, only to find she could not keep it as she lives in a block of flats.
But the signing of Fer, who has two caps for his country, is unlikely to prompt the departure of Marouane Fellaini during the January transfer window, according to Sky sources.
The Belgium international's impressive form this season has attracted widespread interest since the transfer window opened, with the likes of Manchester United and Chelsea reported to be leading the chase.
But Fellaini, who is reported to have a £22m buyout clause in his contract, appears likely to be staying at Everton at least until the end of this season.