Valtteri Bottas will stay at Williams in 2017 as the team promote Canadian rookie Lance Stroll as his team-mate.
Bottas, who has raced for Williams since his debut in 2013, had been of interest to Renault but BBC Sport has learned he will not be moving.
Stroll, who is 18 this month, won this year's European Formula 3 title and has been prepared for his graduation with a series of tests in old Williams cars.
Stroll's father is Canadian billionaire businessman Lawrence Stroll.
Williams' Formula 1 line-up is to be announced in the days following next weekend's Mexican Grand Prix.
A Williams spokeswoman refused to comment.
Finland's Bottas has emerged as one of the leading members of the new generation of drivers in F1.
Stroll is regarded as having potential but his path to an F1 seat has also been eased by him bringing millions of pounds of budget to the team in return for a drive.
Renault are now the only major team without a confirmed driver line-up for 2017.
Nico Hulkenberg's decision to join them from Force India was announced last week but the identity of his team-mate has not yet been decided.
The leading contenders are considered to be Renault's current driver Kevin Magnussen and their reserve driver, the Frenchman Esteban Ocon, who is currently racing for Manor.
Ocon is contracted to Mercedes, who loaned him to Renault this year, and they may instead prefer him to race a car with one of their engines at Force India.
Renault's other 2016 race driver, Jolyon Palmer, is also a possibility at Force India and has an outside chance of retaining his position at his current team.