Postma has made just two substitute appearances for David O'Leary's side so far this season.
"I know I'm becoming a better keeper. I'm improving all the time," he told the club's official website.
"I'm delighted to get this sorted. Thomas has been outstanding, I have no complaints. I'll wait for my chance."
"I haven't played that many games but when you know you're at a club where things are done properly, and where we are undoubtedly on the way up, you want to be a part of it. Why would I want to move?
"I'm very happy here at the club. I'm settled. I have a great life and I love the area. Everything is positive."