My Lutheran Service Book and Hymnal says that the words were written (in German) by Martin Luther (1483-1546.) The English words were written by Frederick Hedge (1805-90). It is based on Psalm 46. The name of the tune is "Ein Feste Burg." I don't know if Luther wrote the tune or if it was around before him.

This song is not what we call "gospel." Gospel music is modern and freer in form than this. We call songs like "A Mighty Fortress" hymns.