Russell made his debut in F1 with the Grove-based squad last year, enduring a tough year as the team was stuck at the back of the field.
The deal puts a halt to all speculation linking Russell to a 2021 seat with Mercedes, who manages the Briton.
However, Russell denies that he is disappointed at the closed door at the reigning world champions.
“No, I’m not disappointed in Mercedes at all,” he said.
“There was nothing more they could do. Claire [Williams] was very firm with her decision that she was not ready to let me go.
And also, since I have a contract with Williams, I have to respect that decision. So I’m here, I’ll be doing everything I can for Williams this year and next year, and let’s see what that holds after that.”
Nicholas Latifi, who made his debut in F1 at the Austrian Grand Prix, will stay on for a second season in F1.
The Canadian has been retained despite having just two grand prix starts to his name. At his first race start, Latifi crossed the line in 11th place.
Williams’ future in F1 beyond 2020 is up in the air, as it announced earlier this year that it has placed the team for sale, with talks already started between a number of interested parties.
Bahrain International Circuit - Winter testing