Lahm stepped down from national duty after leading Germany to World Cup glory in Brazil.
And Bayern Munich colleague Schweinsteiger takes up the mantle, having amassed a wealth of experience across 108 caps.
The 30-year-old made his debut against Hungary in 2004 and will lead Germany into a qualification campaign for Euro 2016, which begins against Scotland on Sunday.
Germany coach Joachim Low hailed the midfielder as a natural replacement for Lahm, and expects him to continue leading Germany through their current glittering period.
"Bastian is an absolute leader, he has always taken responsibility for the national team, on and off the field," Low said.
"I have full confidence in Bastian. But it is not just me - the whole sporting management share my faith.
"Above all, he unites all players behind him - no matter what age, no matter what club they play for - I know Bastian is always there when I need him.
"He will be a great and worthy captain of our national team."
Goalkeeper Manuel Neuer is set to captain Germany on Wednesday in a friendly against Argentina, a repeat of July's World Cup final.
Low has called versatile Hoffenheim midfielder Sebastian Rudy into his squad as doubts remain over the fitness of Jerome Boateng and Sami Khedira.
Mesut Ozil and Mats Hummels are also set to miss out due to injury.