Official comment
File > Library > Backup Library on the old computer.
File > Library > Restore Library on the new computer.
If you're not moving the music through the backup process (which I personally do NOT recommend because it changes the structure of the folders), then copy all your music in the same folder structure from old > new.
After the library is restored, your music will be missing the songs - use my batch relocation technique here to find one song and because only the parent location has changed, the relocation will be done in moments.
The cloud sync should recognize that the database is the same, just on a new computer.