The 23-year-old is set to undergo a medical at Carrow Road after the two clubs agreed an €8 million transfer fee for the highly rated footballer.
Fer is going to become second Dutch player to arrive at Norwich this summer, with the Canaries having already signed Ricky van Wolfswinkel from Sporting Lisbon.
The Netherlands international was on the verge of joining Everton in January 2013, but the deal fell through as he was unable to successfully complete medical examination.
Fer has since continued with scintillating showings in Dutch Eredivisie and it looks as though he will be moving to English Premier League after all.
The highly rated midfielder came through the youth ranks at Feyenoord and went on to join Twente in the summer of 2011. He has managed a total of 27 goals in 163 league appearances for the two sides.