The 29-year-old was the subject of months of speculation as his contract ran down. His old deal was due to expire at the end of the season, which would allow him to leave as a free agent.
However, the Gunners have successfully negotiated a new contract with the Germany international, who will now earn £350,000 a week before tax; more than any other player at the club.
The north London club have been busy in the January window, with winger Alexis Sanchez joining Manchester United in a swop deal for Henrikh Mkhitaryan, before Pierre-Emerick Aubameyang signed from Borussia Dortmund for a club record fee.
Manager Arsene Wenger could also lose striker Olivier Giroud before the transfer deadline on Wednesday night. The Frenchman is reportedly close to a move to Chelsea.