From Ancient Greek βῐ́ος ("life") (ultimately from Proto-Indo-European *gʷeyh₃- ("to live")) + γένεσις (ultimately from Proto-Indo-European *ǵénh₁tis ("birth; production")). The words biogenesis and abiogenesis were both coined by English biologist Thomas Henry Huxley (1825–1895) in 1870 (see the quotation).
The word biogenesis was first used by English physiologist and neurologist Henry Charlton Bastian (1837–1915) around 1869 to mean “life-origination or commencement” in an unpublished exchange of correspondence with Irish physicist John Tyndall. However, in an 1871 book, Bastian announced he was adopting a new term, archebiosis, because of the confusion that might be caused by Huxley’s use of biogenesis with a different meaning.