Hamilton was announced on Tuesday as testing positive for Covid-19, leaving the team to hastily rearrangement a new team-mate for Valtteri Bottas.
Russell has been released by Williams in order to join Mercedes in Bahrain, becoming just the fifth driver to race for the German manufacturer in Formula 1 since its inception in 2010, and the third Briton to represent Mercedes-Benz in F1 after Sir Stirling Moss and Lewis Hamilton.
A thrilled Russell said: “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.
"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.”
Explaining Russell's appointment, 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, who will be a demanding reference for him."
Wolff added: "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."
Russell has been a member of the Mercedes-Benz junior programme since 2017, when he won the GP3 Series championship as a rookie, before repeating the feat in Formula 2 in 2018.
Aitken, meanwhile, is to make his F1 debut after serving as Williams' reserve driver.
The 25-year-old Briton said: “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.
"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.”
Aitken drove the FW43 in an FP1 session earlier in the season at the Styrian Grand Prix, while he has also been competing in F2 this year, scoring two podiums and eight other points finishes.
Williams acting team principal Simon Roberts said: “Our long-term partnership and George’s affiliation with Mercedes is no secret, and so I’m delighted George has this unique opportunity to join Mercedes.
"We have been working hard to ensure that an agreement could be made with Mercedes to allow him this fantastic opportunity.
"George very much remains a Williams driver and we look forward to him returning to us fresh from this experience and wish him a successful race this weekend.
“We are also thrilled this means we are able to give another British talent in Jack Aitken the opportunity to make his Formula One race debut.
"Jack joined Williams at the start of this season, and despite Covid-19 restrictions meaning we haven’t been able to interact with him as much as we would like, he has quickly become a much-liked member of the team.
"We look forward to seeing him build on his previous experience driving the car in practice, to see what he can do in a qualifying and race situation.”
GPFans is a multi-platform, multi-language brand dedicated to Formula One coverage. We bring you all the ins and outs of the sport, 24/7, everything from up-to-the-minute news and features to the latest viral stories and clips.
We believe that a new generation of exciting, outspoken drivers will make F1 more popular than ever before, and we want to give our users access to as much of their heroes as possible, on and off the track. From Lewis Hamilton to Max Verstappen, Daniel Ricciardo to Sebastian Vettel, we provide in-depth analysis of every every Grand Prix in the season, from Australia to Abu Dhabi.
With Formula One under the new ownership of Liberty Media, how the sport is being covered is evolving, and GPFans will look to be at the heart of this progression into new media, as one of the fastest-growing sites covering the king of motorsports.