The 30-year-old Schweinsteiger, who has won 108 caps and scored 23 goals for Germany, will not lead the team in Wednesday's friendly rematch of the final against Argentina due to injury.
The Bayern Munich midfielder, who is the most experienced player in the squad since the departure of Lahm, will also miss Sunday's Euro 2016 World Cup qualifier against Scotland
"Bastian is the absolute leader and he has always shouldered responsibility for the national team on and off the pitch." coach Joachim Loew told reporters.
"I know Bastian is always there when we need him. He will be a great and worthy captain of our team. He is a legitimate successor to Philipp."
Loew also announced a late call-up, bringing in midfielder Sebastian Rudy with Jerome Boateng and Sami Khedira doubtful for the Argentina game and Mesut Ozil and Mats Hummels ruled out.
Loew also said former VfB Stuttgart coach Thomas Schneider would be his new assistant, succeeding Hansi Flick, who becomes the federation's sports director.
"The challenge with the national team is a great one," the 41-year-old Schneider said. "I am honoured that both the DFB and Joachim Loew trusted in me."
"I know Joachim Loew since my time as a player at Stuttgart and already then I noticed how similarly we thought about football," said Schneider, whose only Bundesliga job lasted less than a season.