The former German international defender landed at Edinburgh Airport on Tuesday.
He is poised to move to the Scottish champions from RB Leipzig having recently fallen out of favour with the Bundesliga side.
The 32-year-old will likely meet up with his new team-mates for their warm-weather training trip to Dubai on 6 January as the Celtic players look to stay fresh during the winter break.
Rodgers has been chasing defensive reinforcements since the last transfer window, and attempted to sign South African centre back Rivaldo Coetzee until the deal broke down over concerns about an injury the player had.
However, as outlined last week, the defender would have to sit out Celtic’s Europa League clash with Zenit St Petersburg, after he appeared for Leipzig in the Champions League against Besiktas.