If you need just file names like:
dir/subdir/file1.txt
dir/subdir2/file2.sql
dir2/subdir3/file6.php
(which I use as a source for tar command) you will also need to filter out commit messages.
In order to do this I use following command:
git log --name-only --oneline | grep -v '.{7} '
Grep command excludes (-v param) every line which starts with seven symbols (which is the length of my git hash for git log command) followed by space. So it filters out every git hash message line and leave only lines with file names.
One useful improvement is to append uniq to remove duplicate lines so it will looks as follow:
git log --name-only --oneline | grep -v '.{7} ' | uniq