Williams have had a slow and ill-handling vehicle this year and are last in one of the worst seasons in the history of a proud British team with nine constructors' and seven drivers' championships.
Who Russell will partner at Williams remains to be seen.
Russell is also on the brink of securing the Formula Two championship, the feeder series to F1, following an impressive debut campaign in which he has won six races.
The Briton leads the F2 title race by 37 points from Alexander Albon with only 48 available in next month's finale in Abu Dhabi.
"It is a huge honour to join a team of Williams' prestige and heritage", he said.
"Formula 1 has been a life-long dream", says Russell. From watching the races when I was a child, it feels surreal that I will now be lining up on the grid, alongside drivers who I have admired for years'.
"I can not wait for Melbourne next year and to join Williams at what we all believe will be the start of an exciting new journey".
Russell tested for Mercedes and its customer team Force India this year but a volatile summer of driver market activity threatened the 2014 McLaren Autosport BRDC Award winner's prospects of graduating to F1.
He will be the first English driver to compete for Williams since Button was handed his debut as a 20-year-old in 2000.
"He is already highly regarded in the paddock and a driver whose career we have been watching for a while.
In the time we have spent with him so far, we believe that he will be a great fit for our team".
"I would like to thank Claire [Williams, deputy team principal] and everyone at Williams for their faith in making this decision, as well as Toto [Wolff, Mercedes team boss] and the team at Mercedes for their fantastic support throughout GP3 and Formula 2".
The two teams share a close relationship with Mercedes supplying engines to the Oxfordshire outfit, while Russell has been on the books of the Silver Arrows since the start of previous year.
Both Stroll and Sirotkin bring huge sponsorship deals from Canada and Russian Federation respectively, but Williams may look to partner Russell with an experienced racer, such as 2018 test driver Robert Kubica.
Russell, 20, has been affiliated with Mercedes since the start of 2017, and is poised to add the Formula 2 title to the GP3 crown he won past year.
George Russell has revealed how an opportunistic phone call set in motion his appointment to the F1 grid in 2019.
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