Although Vandoorne is contracted to Mercedes as the reserve driver and is scheduled to be at the circuit this weekend after completing pre-season testing for the manufacturer's Formula E marque in Valencia over the past week, Russell was the preferred option to make the step up.
Hamilton team-mate Voltaire Bots should be looking for his third win of the year in his vehicle, having won 13 of 15 runs this season.
"Firstly, I want to say a huge thank you to everybody at Williams for giving me this opportunity", Russell said.
Russell is managed by Mercedes and has been linked to the team as a potential replacement for Bottas in 2022, but Bottas said he does not see this weekend as a showdown between the two.
"A big thank you also to Mercedes for putting their faith in me", added Russell.
"Obviously, no one can replace Lewis, but from the moment I get in the auto I will give my all for the team in his absence".
What are your overall assessments on last weekend’s race
"Apart from mild symptoms, he is otherwise fit and well, and the entire team sends him its very best wishes for a swift recovery", the team statement said. I'm really looking forward to the opportunity and can't wait to get off track this week.
Jack Aitken says he is "over the moon" after being handed his Formula 1 debut for the Sakhir Grand Prix weekend, insisting he has been ready to make the step for some time.
Mercedes team principal and Russell's boss for the weekend Toto Wolff thanked Williams for their continued cooperation.
Williams' George Russell is set to take Hamilton's seat, surprising many, but bringing joy to more.
The timing of the positive test means it will be a close run thing as to whether whether Hamilton will be able to get back in the cockpit for the final race of the season which takes place the following week. George has had a great impact with Williams this year, helping them climb to the top of the grid, and I am hopeful that he will be gifted with a strong performance alongside Voltaire, who will be a contender for him. We have been working hard to ensure that an agreement could be made with Mercedes to allow him this fantastic opportunity.
Bottas, who has won two races to Hamilton's 11 this year, said his main aim was to finish this season with some good results.
Germany's Mick Schumacher, son of seven-times champion Michael Schumacher and announced on Wednesday as a Haas driver for 2021, can seal the Formula Two title in this weekend's finale.