The music in Tom Clancy's The Division is composed by Ola Strandh. In the 2nd Division podcast, he talks about creating the music for the game.
The music in Tom Clancy's The Division 2 is also composed by Ola Strandh.
Within the game, you will hear music coming from NPCs playing instruments or from radios.
Other soundtracks that he has composed are World in Conflict, Ground Control 1 and 2.