Nasr, 22, already has previous F1 experience: he has competed in four Grand Prix practice sessions for Williams this year as part of his duties as test and reserve driver, and has also tested for the team on two separate occasions at Bahrain.
He won the British Formula 3 championship in 2011 and has competed in GP2 for the past three years. He currently lies second overall in this year's championship, having claimed four wins and nine podiums.
“We have been following Felipe’s career path for some time now, and he fully deserves his position in Formula One having had a very successful career in junior categories," Sauber team principal Monisha Kaltenborn said.
"We are happy that he will be driving for our team next year. This means that Brazil will have one more young and talented driver in the sport."
Nasr added: "It is a very important step in my career to sign with the Sauber F1 Team for the 2015 Formula One World Championship. This is an unforgettable moment that I owe to all of those who have supported me - my family, my friends, my sponsors, my teams and my country.
"Today the dream has come true. Sauber was responsible for the arrival in F1 of great names such as Felipe Massa, Kimi Raikkonen, Robert Kubica and Sebastian Vettel. I am proud now to also be part of this racing family. I had a wonderful year at Williams Martini, where I learned a lot and prepared myself to be a race driver in Formula One.”
The deal, which will see Sauber sporting the logos of Banco do Brasil - one of Nasr's partners - during the 2015 campaign, leaves currents drivers Adrian Sutil and Esteban Gutierrez without a confirmed drive for next season.
Sauber announced they had signed Ericsson for the 2015 season on the Saturday of this year's United States Grand Prix.