Löw praised Schweinsteiger's "immense experience" at a Düsseldorf press conference, saying that the two had worked together for 10 years.
The 30-year-old Schweinsteiger is a "very good communicator" who is "highly accepted in the team," Löw said. He will hold the captaincy for two years.
"When he was needed, Basti was always there," said Löw, using his pet name for the midfielder. "I regard him as a worthy successor to Philipp Lahm."
The outgoing captain, also 30, announced his retirement from international football after July's World Cup victory, having scored five goals in 113 appearances.
The national team will now focus on the next challenges, Löw said, describing the new captain as "blooming with ambition" to take the team forward to the 2016 UEFA European Football Championship.
Löw played down Schweinsteiger's recent injuries, saying that they shouldn't be an obstacle to his holding the captaincy. He trusted him "absolutely" to make the right calls on the way, he added.
From skier to soccer pro
Forsaking a promising career as a skier, Schweinsteiger signed with Bayern Munich as a youth team player in 1998 and worked his way up the ranking to become a dominant club and national player.
He has been capped 108 times and scored 23 goals for the Germany national football team since making his debut in 2004.
In other changes to the national team set-up, Thomas Schneider replaces Hans-Dieter Flick as assistant chief trainer. Schneider is well known to Löw, having played under him when he coached VfB Stuttgart in the mid-1990s.
Flick joined the national team in 2006 when Löw took over as head trainer. He'd been instrumental in achieving the victory in Brazil and would be greatly missed "in sporting terms and as a person", Löw said in his first press conference since the World Cup ended.
Löw, 54, had already extended his own contract until 2016 before the World Cup. After reaching the pinnacle of his career to date, there had been speculation that he might try to terminate his contract prematurely.
The coach assured in late July that he would honour the obligation, saying on the website of the German Football Association (DFB), "I'm as motivated as I was on my first day at the DFB".