Rosberg, who drives under the German flag despite being the son of Finnish former F1 world champion Keke Rosberg, moved to 12th in the world championship standings after his second-place finish at the Singapore Grand Prix on Sunday.
Team principal Frank Williams described the German as "one of the most capable drivers in the sport", adding that Japan's Nakajima was "getting stronger all the time".
He said: "I am delighted to be able to maintain continuity with our drivers."
Nakajima, also 23, made his debut when he replaced the retired Alexander Wurz in last season's final race, and is also following in the footsteps of his father Satoru Nakajima in Formula One.



