The Eredivisie side previously secured the services of Warner Hahn for the position between the sticks, while last year's No.1 Erwin Mulder is still under contract at Feyenoord, too.
They were keen to add another shot stopper to their squad, though, and have now found their man in the 28-year-old Vermeer, who has signed a four-year deal with Feyenoord.
"A number of clubs showed an interest in signing me, but Feyenoord were the most interesting option for me," the goalkeeper commented on his transfer.
"Feyenoord are a big club with a loyal fanbase. And Feyenoord are very ambitious. I cannot wait to get started."
Vermeer came through the ranks of the Ajax youth academy and has made over 100 Eredivisie appearances for the reigning Dutch champions.
He had lost his starting berth at Ajax to Jasper Cillessen last season.