Simple (and outdated, check out http://www.nexusmods.com/fallout4/mods/2990/?) mod, which replaces some of Fallout 4 ambient music with Fallout 1's ambient.

INSTALL:
To install just put "music" folder into your Fallout 4 data folder.
Also you need to change 1 line in Fallout4.ini (C:\Users\<yourname>\Documents\my games\Fallout4)
change " sResourceDataDirsFinal=STRINGS\, "
to look like: "sResourceDataDirsFinal=STRINGS\, MUSIC\"
To uninstall just delete music folder, or only those files.

Music list:
-Metallic Monks (BoS)
-Khans of New California (Khans)
-Vats of Goo (Fallout 1 intro/Mariposa)
-Desert Wind (Wasteland)
-Vault of the Future (Vault 13)
-Industrial Junk (junktown)
-City of the Dead (Necropolis)
-Second Chance (shady sands)
-City of Lost Angels (boneyard)
-Underground Problems (Caves)
-Acolytes of the New God (the Cathedral)

Optional (Fallout 2) music:
-Biggest Little City in the World (New Reno)
-Many Contrasts (San Francisco)
-Gold Slouch (Redding)

Music created by Mark Morgan, uploaded with his permission.