The 50-year-old took charge at De Kuip in 2011, but with his contract due to expire in the summer, he has decided that the time is right for him to move on.
"I've worked well working closely with the players, the staff and all the others here at the club. I've been enjoying myself here from day one. The decision not to sign [a new deal] is one that I've made purely by feeling," he told the club's official website.
"Feyenoord deserve to have certainty over their future. I'm working with the group to reach a beautiful end result and bring three fantastic years together to a close."
The Rotterdam-based outfit are currently fourth in Eredivisie.