The story
Coined by Dano-French geographer Conrad Malte-Brun in 1810 (as langues indo-germaniques) and popularized in German (as indogermanisch/Indogermanisch), especially following J. Klaproth's 1823 Asia polyglotta. At the time the term was coined, the Celtic languages were not yet considered Indo-European, and the Tocharian languages were not yet discovered; even after the inclusion of Celtic, Germanic remains the northwesternmost family (thanks to Icelandic). By surface analysis, Indo- + Germanic.
Etymology from Wiktionary, CC BY-SA 4.0.