1852, from German umlaut "change of sound," from um "about" (from Proto-Germanic umbi, from PIE root *ambhi- "around") + laut "sound," from Old High German hlut (from Proto-Germanic *hludaz "heard, loud," from suffixed form of PIE root *kleu- "to hear"). Coined 1774 by poet Friedrich Gottlieb Klopstock (1724-1803) but first used in its current sense "modification of vowels" 1819 by linguist Jakob Grimm (1785-1863).
The scribal use of umlaut marks in German began 14c. as the pronunciation of some sounds simplified, to indicate the older ("proper") pronunciation; originally it was a full letter -e- above a -u- (later also added to -a- and -o-).
When the umlauted diphthong came to be pronounced as a single vowel sound ü, the e was then written over the u by many scribes in order to indicate the proper pronunciation of what had become a monophthong. ... Our "umlaut marks" are simply the vestiges of the two broken strokes of the Gothic-script e. [John T. Waterman, "A History of the German Language," University of Washington Press, 1976]