The influential midfielder will take over the captaincy armband from Philipp Lahm, with Manuel Neuer as his new deputy.
Lahm opted to say farewell to the national team after skippering it to World Cup glory in Brazil this summer and Low feels Schweinsteiger is the ideal man to succeed his Bayern Munich teammate.
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"Bastian is a real leader and he has always taken his responsibility seriously with the national team, both on and off the pitch," Low said at a press conference. "I have a lot of faith in him and so do the rest of the technical staff. He unites all of the players around him, irrespective of their age and which team they play for.
"Schweinsteiger is always there when we need him. He will be a great and worthy captain for the national team."
The 30-year-old midfielder has made over 100 appearances for Germany since making his official debut in 2004.
Schweinsteiger will miss the upcoming international friendly against Argentina due to injury, with Manuel Neuer wearing the armband instead in the rematch of the World Cup 2014 final.