The soundtrack for NHL '99 is composed by Jeff van Dyck, along with a trimmed down version of Noise Therapy's song "Down" for the Menu Track #5. I obtain the tracks from a CD of the PC version of the game and there are seven tracks, five are Menu Themes and the other two are Qualify and Awards Themes. Out of curiosity, I downloaded the Nintendo 64 version of NHL '99 ROM to see if the music was the same and found it has a different Introduction Theme—the PC version has a David Bowie song, which I omitted—and an extra Menu Theme so I included both of those. There isn't much to the titles, I pretty much just left them as they were labeled "Menu Tracks 1-5." From what I've read, a couple of the tracks were also used in later installments of the series(NHL '06 and NHL '09). I was surprised that the music is actually pretty darn good(I mean, an old NHL game having good original music?). I'm really diggin' the Menu Track 4, it has some catchy riffs, and the Main Menu Track for the N64 version is also a really good song.
And there we have it, both FLAC and MP3 versions are uploaded so enjoy!