"A partnership like this between Formula One and football has never existed before in this form, yet there are numerous commonalities and possible synergies," said Sauber Chief Executive Monisha Kaltenborn in a statement.
"The Sauber F1 Team and Chelsea FC are dealing with many of the same sporting and commercial topics and we want to strengthen each other in these areas."
Sauber had the mysterious inscriptions "out of the Blue" and "True Blue" on the engine covers of their cars in the last two races in China and Bahrain without saying what the words signified.
The Ferrari-powered team said that, in concrete terms, the partnership would include the sale of merchandise and the exchange of sports science know-how.
Both sides will feature the other's logo with the aim of increasing their market presence outside their respective sports.
Chelsea, currently managed by Swiss-born Italian Roberto Di Matteo, will present the Sauber logo at home matches on advertising boards at the stadium and on interview walls.
"Conversely, the football club benefits from Formula One's television reach which, compared with the Premier League, is much higher and more international," said Sauber.
"Particularly in Asia, Formula One enjoys enormous TV presence and, not least thanks to Sergio Perez, is currently captivating more and more fans in Latin America as well."
Sauber's two drivers are Mexican Perez and Japan's Kamui Kobayashi.
Chelsea Chief Executive Ron Gourlay said Sauber, as the fourth oldest team on the starting grid, reflected Chelsea's ideals.
"In a year when Chelsea celebrates 20 seasons as a Premier League team, Sauber does so as a Formula One team," he said.
"We share many philosophies when it comes to how the respective organisations are run, from the development of young talent to constantly striving for success.
"This partnership will benefit us both greatly, with the potential to create unique commercial opportunities," he added. "It is a shared vision to unite the two most attractive sports in the world."