Ozil had been omitted from the team that sensationally defeated Sweden 2-1 in the last outing but takes his place in the starting XI after Muller struggled to make his mark against the Swedes.
The Arsenal playmaker will be joined in the German midfield by Leon Goretzka, who is replacing Julian Draxler, and Marco Reus, with Low opting for a change of approach in his side's ultimate group game.
Behind them, Toni Kroos continues after his last-minute stunner that sealed three points against Sweden and he will be partnered by Sami Khedira, who resumes his place thanks to a Sebastian Rudy injury.
Niklas Sule comes into defence in place of the suspended Jerome Boateng, with Jonas Hector, Joshua Kimmich and Mats Hummels, who is back in for Antonio Rudiger, completing the backline.
Timo Werner will continue to plow a lone furrow in attack, with Manuel Neuer captaining the team from the goalkeeper position.
Defending champions Germany are in need of a win against South Korea if they are to book their place in the knockout stage of the competition.
Low's side recovered from their shock opening defeat to Mexico by clinching a last-minute win against Sweden and, with the Swedes also on three points, they will be aiming for victory against South Korea to boost their chances of progression.
A last 16 encounter with one of Brazil, Switzerland or Serbia is the prize that awaits the teams that progress from Group F.
Germany XI: Neuer: Kimmich, Sule, Hummels, Hector; Khedira, Kroos, Goretzka, Ozil, Reus; Werner.
South Korea XI: HW Jo; Y Lee, YS Yun, C Hong, YG Kim, HS Jang, JC Koo, WY Jung, JS Lee, SM Moon, HM Son.