Bottas will make the switch to Alfa Romeo next year after five seasons alongside Hamilton at the Silver Arrows.
The 32-year-old Finn, who finished third at Sunday’s Dutch Grand Prix, will replace Kimi Raikkonen.
The 2007 world champion, 41, will retire from Formula One at the end of the year.
It is expected that Russell’s elevation from Williams to Mercedes will be announced on Tuesday.
Bottas, a nine-time race winner, said: “A new chapter in my racing career is opening.
“I’m excited to join Alfa Romeo for 2022 and beyond for what is going to be a new challenge with an iconic manufacturer.
“I’m grateful for the trust the team has put in me and I cannot wait to repay their faith. I’m as hungry as ever to race for results and, when the time comes, for wins.
“I am looking forward to getting to know the rest of the team I am going to work with, building relationships as strong as the ones I have at Mercedes.
“I am proud of what I have achieved in Brackley and I am fully focused on finishing the job as we fight for another world championship, but I am also looking forward to the new challenges that await me next year.”
Along with his nine wins, Bottas has secured 17 poles and 63 podiums. The Finn proved an able deputy to Hamilton after he was signed to replace Nico Rosberg following the German’s retirement days after clinching the 2016 world title.
Hamilton has spoken repeatedly of his preference for Bottas to stay, but the Mercedes hierarchy have looked to the future by hiring the highly-talented Russell.
Russell’s move to take up the hottest seat in the sport will see him form a tantalising all-British line-up with Hamilton, 36.
His promotion comes after three seasons with Williams and a hugely impressive stand-in display for a Covid-hit Hamilton in Bahrain last December.
Russell, from King’s Lynn, also produced a memorable qualifying lap to put his uncompetitive Williams on the front row of the grid for last month’s Belgian Grand Prix, duly taking second following the two-lap race run behind the safety car.
The identity of Bottas’ team-mate next year is uncertain, with Alfa Romeo’s current driver, Antonio Giovinazzi, former Red Bull man Alexander Albon and Nyck De Vries, the Formula E world champion, all in the frame.