"a seat with a back, intended for one person," early 13c., chaere, from Old French chaiere "chair, seat, throne" ... from Latin cathedra "seat" (see cathedral).
Figurative sense of "seat of office or authority" c. 1300 originally was of bishops and professors. Meaning "office of a professor" (1816) is extended from the seat from which a professor lectures (mid-15c.). ...
The etymology is much more obvious in Romance languages: see e.g. the Spanish word catedrático.
Note that there's a specific type of chair which is also used figuratively to refer to the authority of the person who is entitled to sit in it: throne. Usage is probably parallel, although digging out examples to demonstrate this would be a non-trivial research project.
I see from comments that there are two opinions about what the question meant by asking about usage. To address the other opinion, in as much as it's not already answered by user2768: professor in British English is reserved to those who hold a chair, which may be an endowed or a personal chair. In American English it is used far more widely. Cognate words in other languages may be used even more widely still: in Spanish, profesor is used for teachers from primary to tertiary education, although as mentioned above there's also a word catedrático which corresponds to the British professor. I would expect that most of the Commonwealth follows the British usage, with the possible exception of Canada, but I would not be surprised to be corrected on this in comments.