Amsterdam-born, Vermeer is a product of the Ajax academy and he progressed through the ranks to make his debut in a UEFA Cup game against IK Start in 2006/07.
He was then loaned out to Willem II, where he gained Eredivisie experience, before returning to Ajax where his breakthrough season came in 2008/09 under new boss Marco van Basten.
During his time with the club he won four league titles and the KNVB Cup, while establishing himself in the Netherlands squad.
In August 2014 Vermeer switched to rivals Feyenoord and was a member of the squad that picked up the Eredivisie title in 2016/17. He also spent six months on loan at Club Brugge in 2018, helping the club to the Belgian Pro League title.
He has five senior international appearances to his name, making his debut and keeping a clean sheet against Germany in 2012.