Llambias' resignation comes a day after Joe Kinnear was confirmed as the club's director of football on a three-year deal.
In a short statement on the club's official website, posted 20 minutes before the release of the 2013-14 season fixtures, Llambias said: "I have had an incredible journey during my five years at the club, including some challenging times. I will reflect with great fondness on my time in the north east and, in me, Newcastle United have a lifelong supporter."
He added: "I want to thank the staff for their hard work, our fans for their support of the club, and wish them all well for the future."
More to follow.