extract using 7zip or winRAR and place in your ~mods folder

Steam\steamapps\common\KINGDOM HEARTS III\KINGDOM HEARTS III\Content\Paks\~mods 

if there is no ~mods folder create it.

Tracklist: 

Promise (FFXIII) - Title Screen

Hisoria Crux (FFXIII-2) - World Map 
Serendipity (FFXIII-2) - Gummi Edit
Feral Link (FFXIII-2) - Gummi Ready
Village and Void Aggr. (FFXIII-2) - Gummi Zone 1
Parallel Worlds Aggr. (FFXIII-2) - Gummi Zone 2 
Eclipse Aggr. (FFXIII-2) - Gummi Zone 3 
Army of One (LR) - Gummi Battle
Blinded by Light (Dissidia NT Version) - Gummi Battle 2
Glory's Fanfare (FFXIII-2) - Gummi Results

Crazy Chocobo (FFXIII-2) - Attractions

Sunset Path (LR) - Twilight Town
Savior of Souls (LR) - Twilight Town Battle 

Savior's Words (LR) - Bistrot
In The Sky That Night (FFXIII) - Bistrot Cook
Glory's Fanfare (FFXIII) - Bistrot Finish
Daddy's Got The Blues (FFXIII) - Bistrot Fail

A Carefree Existence (LR) - 100 Acre Wood
Chocobo of Pulse (FFXIII) -100 Acre Wood Minigame Phase 1
Chocobo de Marimba (LR) - 100 Acre Wood Minigame Phase 2
Chocobo Rodeo (FFXIII) - 100 Acre Wood Minigame Phase 3

Fang's Theme Distant Worlds Ver. (FFXIII) - Olympus 1
Saber's Edge (FFXIII) - Olympus 2 
Divine Conflict (FFXIII-2) - Olympus Battle 1
Lightning Returns (LR) - Olympus Battle 2

Sazh's Theme (FFXIII) - Toybox 
K.O. (LR) - Toybox Battle

Sunleth Waterscape (FFXIII) - Corona 1
Blinded by Light (FFXIII) - Corona Battle 1
Archlyte Steppe (FFXIII) - Corona 2
Equilibrium (LR) - Corona Battle 2
Ouroboros Festival (LR) - Corona Dance
Glory's Fanfare (FFXIII) - Corona Results

All or Nothing (FFXIII-2) - Classic Kingdom Menu

Hanging Edge (FFXIII) - Monstroplis 1
Paradox (FFXIII-2) - Monstroplis 2 
Death Game (LR) - Monstroplis Battle

New Bodhum (FFXIII-2) - Arendelle 1
New Bodhum Aggr. (FFXIII-2) - Arendelle Battle 1
Academia (FFXIII-2) - Arendelle 2
Chaos (LR) - Arendelle Battle 2
Starting Over (FFXIII-2) - Frozen Slider
Salvation's Fanfare (FFXIII-2) - Frozen Slider Results

The Gapra Whitewood (FFXIII) - Caribbean 1
Eternal War (FFXIII-2) - Caribbean Battle 1 
Nova Chrysalia (LR) - Caribbean 2 
Divine Love (LR) - Caribbean Battle 2
Sulyya Springs - Caribbean 3

Plains of Eternity (FFXIII-2) - San Fransokyo 1
Full Speed Ahead (FFXIII-2) - San Fransokyo  2
High Voltage (LR) - San Fransokyo Battle
Plains of Eternity Aggr. (FFXIII-2) - Flash Tracer 
Blessed Fanfare (FFXIII-2) - Flash Tracer Results

Crimson Blitz (LR) - Battlegate 1
Noel's Theme guitar demo (FFXIII-2 Plus OST) - Battlegate 2
Last Hunter (FFXIII-2) - Battlegate 3

Yeul’s Theme (FFXIII-2) - The Final World

Eclipse (FFXIII-2) - The Keyblade Graveyard

The Ark (LR) - Scala Ad Caelum
Paradigm Shift (FFXIII-2) - Scala Ad Caelum Battle

Hope's Theme (FFXIII-2) - Radiant Garden (Limit Cut) 
The Ark OST Exclusive Ver. (LR) - Garden of Assemblage