The 32-year-old has been at Carrow Road since joining Norwich in 2001.
“I am obviously delighted to be at this special club for another year,” Drury told the club’s official website.
“Things are going well at the moment and the gaffer and coaching staff have got something special going on and I want to be part of it.
“The fans have been great to me since I’ve been here and support us in great numbers both home and away.”
“He has been great for me since I’ve been here and he’s a terrific professional and a top player,” said Newcastle boss Paul Lambert.
“To be at a club for almost 10 years is an achievement in itself and I am delighted to sign him for another year.”
