Speculation has been rife in recent weeks linking the Danish international with a move away from the Emirates, with the 23-year-old also rumoured to be in line for a move to Stoke City.
However Bendtner has now been reunited with manager Steve Bruce, who also took the striker on loan during his time in charge at Birmingham City.
The Dane - who has scored 22 times in 98 appearances for Arsenal - played under Bruce on loan at the Bluenoses throughout the 2006-07 season that culminated in promotion to the Premier League.
Bendtner, who signed a five-year contract with Arsenal in 2007, will be hoping to rejuvenate his career at Sunderland, following the example of Manchester United striker Danny Welbeck whose flourished while on loan under Bruce last season.
Speaking to the club’s official website, Bruce said: "I've had the privilege of working with Nicklas previously. I had him as an 18-year-old and he helped clinch promotion for Birmingham.
"He's an outstanding talent and is a big, physical presence who will lead the line magnificently for us."
Bendtner become’s Sunderland’s third attacking signing of this summer’s transfer window, following the arrivals of Connor Wickham and Ji-Dong Won at the Stadium of Light.