Gundogan, who featured in all five games for Germany at EURO 2024 with his last appearance coming in their quarter-final defeat by eventual champions Spain, retired from internationals after winning 82 caps last month.
Having made his debut for Germany in 2016, Kimmich has made 91 appearances for the national team.
Kimmich, who plays as a right-back and midfielder for Bundesliga giants Bayern Munich, will lead Germany when they host Hungary in the Nations League in Dusseldorf on Saturday.
"The captain places the team's opinion with the coaching team. He was the logical successor. He leads the way with his mentality," Nagelsmann told reporters.
Real Madrid centre-back Antonio Rudiger and Arsenal forward Kai Havertz will be vice-captains.
"We have a very good mix with these three players," Nagelsmann added.
Barcelona captain Marc-Andre ter Stegen will be the number one goalkeeper for Germany following Manuel Neuer's retirement from internationals last month. Ter Stegen has been capped 40 times for Germany.
Neuer retired from national duty after playing 124 games since making his debut in 2009, during which he was awarded the golden glove when Germany won the 2014 World Cup.
"Marc is number one. And deservedly the number one," Nagelsmann said. "He has performed well for several years. He has been captain at Barcelona for several years and is the undisputed number one with very, very good performances.
"And he will also fulfil that role for us. That's why he's the clear number one."
Germany will also play Bosnia & Herzegovina and the Netherlands in League A Group 3 of the Nations League.