"The Polish goalkeeper staying is recognition and a prize for his great season between the sticks for Barça, after an unexpected arrival in a strange context," wrote the Catalan club in a statement.
Szczesny had retired from football when Barcelona signed him in October to replace injured stopper Marc-Andre ter Stegen, who was ruled out for most of the season with a ruptured patella tendon.
The 35-year-old impressed as Barcelona won La Liga and the Copa del Rey, with Ter Stegen only returning to the squad in the final weeks of the season.
Szczesny's decision to stay and Barça signing goalkeeper Joan Garcia from Espanyol earlier in the summer casts doubt over Ter Stegen's future at the club.
The German international, 33, commands a high salary at Barcelona, and Spanish media reports the financially struggling club would like to make savings in that regard.
Barça signed Garcia from Espanyol for €26.34 million (£22.6 million) on a six-year deal in June, and also still have another goalkeeper in Inaki Pena on the books.