Alfa Romeo have scored 10 points this season and sit ninth in the constructors' championship
Bottas, who joined from Mercedes in 2022, was under contract for next season but there had been some doubt about the future of his team-mate.
Representative Alessandro Alunni Bravi said the team had chosen "stability" as they continue their transition into the factory Audi effort by 2026.
The team are ending their relationship with Alfa Romeo after this season.
They will race under a new name next year but this has not yet been revealed. Although Audi is already a part-owner, the German car giant's name is not expected to be used until it officially enters F1.
Bravi said: "Valtteri and Zhou are drivers of known talent and skill and they work really well together: they are well-matched and can push each other.
"Valtteri has taken a real leader's role within the team, pushing us all to give our best; Zhou has made impressive steps forward in the last two years and we expect him to continue on this trajectory in 2024."
Reserve driver Theo Pourchaire will also continue with the team.
Bottas, whose contract ends next season, said: "I have a feeling we have an exciting journey ahead of us. There is an impressive amount of work going on behind the scenes, in [the team's base in] Hinwil and beyond, and now that the line-up is set for next year, we can focus fully on improving, starting this weekend in Singapore already.
"Every step forward we make is a step forward for this year and next, so we are motivated to give everything we have every time we're trackside or at the factory."
Zhou said he was "grateful for the trust" Sauber had shown in him and that he was "excited" at the prospect of racing at his home grand for the first time as China returns to the F1 calendar next year for the first time since the pandemic.
Alfa Romeo/Sauber have had a difficult year and are in ninth place out of 10 teams in the constructors' championship, one point behind Haas with eight races remaining this season.
-- Courtesy of BBC Sport