The 23-year-old Poland international joined the club from Legia Warsaw in 2006 and has been manager Arsene Wenger's first-choice goalkeeper since breaking into the first team during the 2010-11 season.
"I've been at this club for over seven years now and I'd just like to take the opportunity to thank everyone for their support towards me during my time here."
Arsenal did not reveal the precise length of Szczesny's new deal, but Wenger said: "I have always believed he is an extremely talented player, with excellent reflexes and good mental strength.
"He continues to grow and improve all the time too, so he has the potential to be even better. He can be an important part of Arsenal Football Club for many years to come."