2014 World Cup winner Hummels and midfielder Brandt have been key figures in Dortmund's run to the Champions League final, where they will face Real Madrid, but Nagelsmann preferred to stick with the team which beat France and the Netherlands in March.
Bayern Munich's Leon Goretzka was also left out of the hosts' 27-man squad - it will be reduced to 26 after the June friendlies against Ukraine and Greece - while his teammate Serge Gnabry was not considered because of injury.
Eliminated at the group stage in the past two World Cups and at the last 16 at Euro 2021, Germany had a poor 2023, winning just three of 11 games which cost then coach Hansi Flick his job.
After losses against Turkey and Austria to end 2023, Nagelsmann named a heavily changed squad for the March friendlies, including bringing in players from Bundesliga champions Bayer Leverkusen and in-form Stuttgart.
Germany impressed as a result with wins over 2022 World Cup finalists France and the Dutch.
Nagelsmann has now brought in Dortmund defender Nico Schlotterbeck and Stuttgart goalkeeper Alex Nubel, one of four keepers named, for Heidenheim's Jan-Niklas Beste and injured Fulham's keeper Bernd Leno.
Bayern's Leroy Sane, who missed the March friendlies through injury, has also been added to the squad.
Nagelsmann said having four keepers was crucial for spreading the workload during the tournament.
"We have nominated four goalkeepers and we will go with four to the tournament. Nubel has deserved the nomination," he said.
"Why four keepers? You can have goalkeepers in training as well and Manuel (Neuer) does not always have to do it. We can control training and spread the load.
"That means 22 infield players. I can live with that very well. We can still do proper training with at least 20 infield players if some are missing."
The announcement, made in downtown Berlin near the famous Brandenberg Gate, included three members of Germany's 2014 World Cup winners from Brazil: goalkeeper Manuel Neuer, forward Thomas Muller and midfielder Toni Kroos.
Barcelona midfielder Ilkay Gundogan will remain captain despite Neuer's return, which Nagelsmann had already confirmed prior to the announcement.
The German FA had already announced 18 of the squad on a one-by-one basis via social media and other sources, reducing the speculation over the final make-up.
The Euros start on June 14th, with Germany facing Scotland in Munich.
Germany go into a pre-Euros training camp in the central village of Blankenhai - where England will be based during the tournament - from May 26th until June 1st.
Four members of the squad: Dortmund's Schlotterbeck and Niclas Fullkrug, along with Real Madrid duo Antonio Rudiger and Toni Kroos, play the Champions League final at Wembley on June 1st and will not take part.
Nagelsmann confirmed the four will join the squad two days after the Champions League final.
Germany will play two pre-tournament friendlies, facing Ukraine on June 3rd in Nuremberg and Greece four days later in Monchengladbach.
Full squad:
Goalkeepers: Oliver Baumann (Hoffenheim), Alex Nubel (Stuttgart), Manuel Neuer (Bayern Munich), Marc-Andre ter Stegen (Barcelona)
Defenders: Waldemar Anton (Stuttgart), Benjamin Henrichs (RB Leipzig), Joshua Kimmich (Bayern Munich), Robin Koch (Eintracht Frankfurt), Maximilian Mittelstadt (Stuttgart), David Raum (RB Leipzig), Antonio Rudiger (Real Madrid), Nico Schlotterbeck (Borussia Dortmund), Jonathan Tah (Bayer Leverkusen)
Midfielders: Robert Andrich (Bayer Leverkusen), Chris Fuehrich (Stuttgart), Pascal Gross (Brighton and Hove Albion), Ilkay Gundogan (Barcelona), Toni Kroos (Real Madrid), Jamal Musiala (Bayern Munich), Aleksandar Pavlovic (Bayern Munich), Leroy Sane (Bayern Munich), Florian Wirtz (Bayer Leverkusen)
Forwards: Maximilian Beier (Hoffenheim), Niclas Fullkrug (Borussia Dortmund), Kai Havertz (Arsenal), Thomas Muller (Bayern Munich), Deniz Undav (Stuttgart)