This mod was originally created by m3Zz, and was updated for version 1.6.0 by me, with the author's permission to post it. You can find the original mod page here. Please endorse the original mod before downloading this updated version.

I now have remade the mod, adding better loops to the songs and also a new level up sound effect.

Also report any bugs that you find that I'll try to fix them as soon as possible.

The following is the description of the original mod, written by m3Zz unaltered:

I have managed to replace the in-game music with the Final Fantasy Tactics soundtrack. :D For the best FFT clone I have seen on PC (except for Emus/Roms and some great FFT hacks). After some days of testing and failing, I could create a full replacement for the Fell Seal in-game music by using "Unity Assets Bundle Extractor" and "Unity".

All 26 music tracks of Fell Seal are replaced, as closely as possible (for shop, troops, menu, prepare etc.) to FFT. Some tracks (battle, boss, dialogue etc.) are selected by my taste, because there wasn't a clearly unique track to take. But I selected the tracks to my best knowledge, belief and love to FFT. I still get goosebumps from those tracks and they remind me of the great time I had so far with the original FFT.

Simply download the WAV (recommended) or OGG version and open the "Readme.txt" for easy extract and replace instructions.

I used original FLACs, converted them to WAV and imported them to Unity. For OGG I used the highest available quality setting by Unity (100).
A list of the Final Fantasy Tactics tracks I took as a replacement (all from the SSCX-10008 OST: https://vgmdb.net/album/26#) can be seen in the Images section. Also plus all track translations in the included Excel XLSX table.

The mod is made with and for Fell Seal v1.0.4 (Steam BuildID 3898173).

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Bonus: Short Tutorial on how I did it

You basically open the vanilla *.assets (e.g. resources.assets for Fell Seal) you want to edit with UABE, export the music WAVs
(you can keep this UABE instance open and running) and replace them by creating a new empty Unity project (with Unity).

Do so with the default scene and import your new WAVs, that you want to use as a replacement. After importing (and possibly a conversion to OGG and adding loop flags, if needed), you simply drag and drop them to the main center 3D window (they should appear on the left list). After that you open "File > Build Settings...", set "PC, Mac & Linux Standalone", press the "Add Open Scenes" button (the single scene should now be listed) and check the "Development Build" box. Now click "Build" and select a folder to export.

Start a 2nd instance of UABE and open the by Unity newly created "XYZ_Data\sharedassets0.assets" (XYZ = game/mod name) of your project. Find the music files, select them all and click "Export Dump" and select a folder for it. Close the 2nd instance of UABE. Now go to the very same folder "XYZ_Data" (of your exported Unity project) and rename the "sharedassets0.resource" to something else (I named it "fftmusic.resource"). Copy this file to your "Fell Seal_Data" folder of your installed game. Now open all exported dumps you made before (e.g. with Notepad++) and edit each "1 string m_Source = "sharedassets0.resource"" line to your new resource filename (as said, mine is "fftmusic.resource", like: 1 string m_Source = "fftmusic.resource").

Now go back to your 1st instance of UABE from the beginning (or reopen the vanilla *.assets you want to alter), select the file/files (I made it one by one) you wanted to replace and click "Import Dump" and select the corresponding dump data you have exported and edited. Select ""File > Save" and again save it to your installed game "Fell Seal_Data" folder, not as "resources.assets" (cause you have this file opened with UABE right now), but e.g. "MODresources.assets". Close the 1st instance of UABE. At last browse to your installed game "Fell Seal_Data" folder again, move the vanilla "resources.assets" (you have just closed with UABE) to somewhere else and rename your just created "MODresources.assets" to "resources.assets". Try it in-game. Have fun. ;)