With Mercedes development driver Russell vacating his seat with Williams for the second race in Bahrain, Jack Aitken will make his Formula 1® race debut with the British team.
Seven-time F1® champion Hamilton was ruled out of contention after testing positive for COVID-19 on Monday, a day after he won the Bahrain Grand Prix.
Despite Stoffel Vandoorne and Esteban Gutierrez being Mercedes' official reserve drivers, Williams agreed to release Russell to the Silver Arrows for the penultimate event of the season.
"Firstly, I want to say a huge thank you to everybody at Williams for giving me this opportunity. I might be wearing a different race suit this weekend, but I'm a Williams driver and I'll be cheering my team on every step of the way," said Russell.
"I see this as a great chance to learn from the best outfit on the grid right now and to come back as an improved driver, with even more energy and experience to help push Williams further up the grid. A big thank you also to Mercedes for putting their faith in me.
"Obviously, nobody can replace Lewis, but I'll give my all for the team in his absence from the moment I step in the car. Most importantly, I wish him a speedy recovery. I'm really looking forward to the opportunity and can't wait to get out on track this week."
Mercedes intend to announce their driver plans for the season-closing Abu Dhabi Grand Prix next week.
Team principal Toto Wolff said: "First and foremost, I wish to thank our loyal partners at Williams for their collaboration and open-mindedness in making it possible for George to race for Mercedes this weekend. The conversations with the team at Williams were positive and pragmatic, and those were the key factors in reaching an agreement.
"It will not be a straightforward task for George to make the transition from the Williams to the W11, but he is race-ready and has detailed understanding of the 2020 tyres and how they perform on this generation of cars.
"George has shown impressive form this year with Williams, playing an instrumental role in their climb up the grid, and I am optimistic that he will deliver a strong performance alongside Valtteri [Bottas], who will be a demanding reference for him.
"This race will mark a small milestone for us, as we see a member of our junior programme compete for the works Mercedes team for the first time.
"We have a job to do this weekend, and the full focus of our sporting efforts will be behind Valtteri and George in order to maximise our points score as a team. But, of course, our thoughts are also with Lewis, and we will be supporting him as much as we can to make a rapid recovery during his period of self-isolation."
Williams reserve driver Aitken took part in an FP1 session at this season's Styrian Grand Prix but has also been competing in Formula Two this year, finishing on the podium twice.
"I'm absolutely over the moon to have the opportunity to make my debut with Williams this coming weekend and I am extremely happy for George to have his chance too," said Aitken.
"I really mean it when I say I've felt very much at home here since I joined Williams earlier this year, so to get my chance to help the team try to achieve that elusive points finish is an extremely satisfying occasion to say the least.
"I'll be doing all I can to prepare in the coming days, but truthfully, I feel like I have been ready since Melbourne. I also want to wish Lewis well in his recovery, and good luck to George getting the chance to drive the Mercedes this weekend."