The Brit, who is almost nailed on to win the F2 Championship in Abu Dhabi, is part of the Mercedes young driver programme.
The 20-year-old has signed a “multi-year agreement” with the team, but will still remain linked to Mercedes.
“It is a huge honour to join a team of Williams’ prestige and heritage,” Russell said.
“I would like to thank Claire [Williams] and everyone at Williams for their faith in making this decision, as well as Toto [Wolff] and the team at Mercedes for their fantastic support throughout GP3 and Formula 2.
“I am incredibly excited to start working with everyone at Grove and to take my first steps as a Formula 1 race driver.
“I cannot wait for Melbourne next year and to join Williams at what we all believe will be the start of an exciting new journey.”
Williams’ deputy team principal Claire Williams was criticised earlier this year for signing Sergey Sirotkin up for 2018.
The Russian was the last man to score a point, having only managed to do so in Monza at the start of September.
Now, though, Williams has said that the team has “always tried to promote and develop young talent at Williams, and George fits that ethos perfectly”.
“He is already highly regarded in the paddock and a driver whose career we have been watching for a while,” she continued.
“In the time we have spent with him so far, we believe that he will be a great fit for our team; his commitment, passion and dedication is exactly what we need to drive the positive momentum building at Grove as we focus on the future.
“We are extremely excited to welcome George and working with him moving forward.”
Will Sergey Sirotkin keep hold of it, or will Robert Kubica come in and take it? If so, Esteban Ocon’s chance of remaining in Formula 1 will vanish. Artem Markelov has also been a name banded about for the second seat.