The club confirmed Fer is on his way to Merseyside to discuss a contract and undergo his medical, and the move is expected to be confirmed within 24 hours.
Everton are thought to be paying around £8 million for Fer, who joined Twente from Feyenoord in 2011 - reports claim they will finance the deal in instalments.
Despite the club's limited financial means, Fer's arrival will not herald the departure of key players such as Marouane Fellaini or Leighton Baines.
Fer has won two senior caps for the Netherlands and was a regular in the U21 side.
He is best known in Britain for buying his girlfriend a £20,000 horse last autumn, only to have to return it because it wouldn't fit in her flat.
He said: "I was serious: he's a lovely horse. It was just not meant to be."