"I am very happy that we found common ground," said Sutil.
"Although I have known for a while where I wanted to go, in the end the negotiations took a bit longer than planned. However, now I will have all the more reason to celebrate during the Christmas season.
"After six good years driving for Force India, with a lot of highlights, it's now time to embark on a new challenge. I am determined to do my part in order to have a successful future together with the Sauber F1 team."
The move marks the first time Sutil has raced for an F1 team other than what is now known as Force India.
He joined the Silverstone based squad in 2007, when it was known as Midland, after impressing it in practice outings during '06, and stayed through its Spyker period into the Force India era.
Sutil eventually lost his seat at the end of 2011, a year marred by an assault conviction following an incident in a nightclub after the Chinese Grand Prix, but he returned for '13.
The 30-year-old's best result in his 109-grand prix career is fourth place at Monza in 2009, when he also qualified on the front row.
Sauber is yet to announce its second driver for 2014.
The team has said Russian teenager Sergey Sirotkin would race subject to getting the necessary Superlicence, but other alternatives are reportedly being considered.