1630s, "public notice," from Late Latin programma "proclamation, edict," from Greek programma "a written public notice," from stem of prographein "to write publicly," from pro "forth" (see pro-) + graphein "to write" (see -graphy).
The meaning "written or printed list of pieces at a concert, playbill" is recorded by 1805 and retains the original sense. The sense of "broadcasting presentation" is from 1923.
The general sense of "a definite plan or scheme, method of operation or line of procedure prepared or announced beforehand" is recorded from 1837. The computer sense of "series of coded instructions which directs a computer in carrying out a specific task: is from 1945.
The sense of "objects or events suggested by music" is from 1854 (program music is attested by 1877). Spelling programme, established in Britain, is from French in modern use and began to be used early 19c., originally especially in the "playbill" sense.