The 23-year-old midfielder is poised to join the Toffees after a fee believed to be in the region of 8.5 million pounds was agreed with the Eredivisie outfit.
The 23-year-old is now expected to travel to Merseyside to undergo a medical and discuss personal terms ahead of an estimated 8.5 million pound move.
The signing will represent David Moyes' first foray into the market this January and comes on the back of watching Kevin Mirallas again succumb to injury in the 2-1 FA Cup win at Bolton.
Fer has netted 10 goals in 29 games since moving to Twente in 2011. He is a product of the Feyenoord youth academy where he spent four years as a professional, accumulating over 100 appearances for the Eredivisie side.
The central midfielder has also represented the Netherlands twice.