The 20-year-old, who has a long-term contract with Williams' engine providers Mercedes, looks set to win the Formula Two championship after taking a 37 point lead with two races to come.
"I feel 100 percent ready," Russell, who will debut in Australia in March, told Reuters in an interview.
"I feel really motivated for the task ahead," added the Briton, who has had to contain his excitement for weeks after being told at last month's Russian Grand Prix that he had got the drive.
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"Formula One has been my lifelong ambition and dream, so to finally get this opportunity... I'm definitely not going to take this for granted."
Hamilton, who can clinch his fifth world championship in Texas next week, is at Mercedes while Norris, 18, will be making his race debut with McLaren in 2019 after competing against Russell in Formula Two.
Williams have had a slow and ill-handling car 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.

George Russell of Great Britain and Mercedes GP walks into the paddock before final practice for the Formula One Grand Prix of Singapore at Marina Bay Street Circuit on September 15, 2018 in Singapore.

Image credit: Getty Images

The tall Russell follows in the footsteps of 2009 world champion and compatriot Jenson Button, who was handed his debut by team founder Frank Williams as a 20-year-old in 2000 and won the title with Brawn GP.
Britons Damon Hill, in 1996, and Nigel Mansell, in 1992, both took their championships with Williams, who have not won a race since 2012.
"We have always tried to promote and develop young talent at Williams, and George fits that ethos perfectly," said deputy principal Claire Williams.
"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."
Williams gave no details about who their other driver would be, but 19-year-old Canadian Lance Stroll looks certain to move to Force India - a team now controlled by his billionaire father Lawrence.
The future of Russian Sergey Sirotkin, who made his debut with Williams this year, remains uncertain with financial considerations possibly coming into play.
Mercedes have yet to secure a seat for young Frenchman Esteban Ocon, who also has a long-term contract with the reigning champions but is set to lose his Force India place to Stroll.
Poland's Robert Kubica, a former grand prix winner, has served as reserve this season and is keen to make a race return after suffering serious hand injuries in a rally crash in 2011. (Reporting by Alan Baldwin, editing by Sudipto Ganguly)
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