With regular skipper Wayne Rooney not called up for the double-header against Germany and Lithuania, Gary Cahill wore the armband for the 1-0 loss to Dortmund.
The Chelsea defender is suspended for Sunday's game at Wembley, allowing Hart - who is currently on loan at Torino from Manchester City - to take up the honour.
"I did have to think seriously because we have a squad now with some emerging leaders," Southgate told reporters on Saturday.
"I've talked before about sharing the responsibility around the squad, and even some of the youngest players coming in have been able to talk openly in front of everybody this week, which is a good sign.
"Joe is our most-capped international. He has shown great maturity in the way he has recovered from his own disappointment last summer.
"It's a good moment for him. He's playing well for his club and his performances for us have been excellent.
"Some people will question a goalkeeper as being captain but I did it with Jack Butland in the U21s and in the end you are looking for the professionalism and impact during the week, not just on a matchday."
Hart has previously captained England, with the first coming against Spain in November 2015.