Blame it on the Greeks or possibly the Germans 1680s, “the histories of individual lives, as a branch of literature,” probably from Medieval Latin biographia, from later Greek biographia “description of life” (which was not in classical Greek, bios alone being the word there for it), from Greek bios “life”. The meaning “a history of some one person’s life” is from 1791. The meaning “life course of any living being” is by 1854. No one-word verb form has become common; biographise/biographize (1800), biography (1844), biograph (1849) have been tried.
It was shortened to biog in 1942 & further shortened to bio in 1961.
-graphy
word-forming element meaning “process of writing or recording” or “a writing, recording, or description” (in modern use especially in forming names of descriptive sciences), from French or German “graphie”, from Greek“graphia” “description of,” used in abstract nouns from “graphein” “write, express by written characters,” earlier “to draw, represent by lines drawn,” originally “to scrape, scratch” (on clay tablets with a stylus), from PIE root *gerbh- “to scratch, carve”