Just drag and drop the "Distance OST" folder into your PAYDAY 2\assets\mod_overrides folder, simple as that.

All credits to torcht and his amazing work on the soundtrack!
https://soundcloud.com/torcht
https://twitter.com/torcht

And here's the game the soundtrack is from, if anyone's interested
http://survivethedistance.com/

Songs used

Anticipation:

Assault:

Control:

Stealth: