The Ukrainian champions have been unable to use their Donbas Arena since Russian-backed forces entered the region in 2014 and were further displaced by Russia's full-scale invasion of Ukraine in 2022.
Since leaving Donetsk, Shakhtar have played domestic matches in Kyiv and Lviv, while hosting European fixtures in Hamburg, Warsaw, Gelsenkirchen, Krakow and Ljubljana.
The move to London comes after Chelsea failed to qualify for European competition following a 10th-placed Premier League finish last season, leaving Stamford Bridge available for Shakhtar's Champions League campaign.
"We are grateful to Chelsea Football Club for the opportunity to host our games at this special venue," Shakhtar said in a statement.
"Stamford Bridge is one of the most famous stadiums in world football, with an incredible history and atmosphere.
"We are convinced that Shakhtar's matches in London will provide unforgettable emotions for Ukrainian and English fans."
Chelsea were formerly owned by Russian oligarch Roman Abramovich, who was sanctioned by the UK government following Moscow's invasion of Ukraine in 2022, triggering the sale of the club to a group led by American investor Todd Boehly and Clearlake Capital.
Stamford Bridge has a capacity of around 40,000.
"Shakhtar have played in countries across Europe and we look forward to welcoming them to London for their Champions League campaign this year," Chelsea said.
"We will be working closely with the Shakhtar team over the coming weeks to ensure that matchdays run safely and smoothly for their team and supporters."