Definition - to end a romance
Break up has been in use as a verb, with a large number of possible meanings, for many hundreds of years. Our earliest record of the word meaning "to end a romance" comes from a 1702 translation of a book about the happenings in the French court (quelle surprise).
For that very day she made a show of melancholy to the Duke; she told him that she could no longer converse with him, as hitherto she had done; because her conscience reproached her continually with her guilt, and represented to her every moment, that she only was the cause that he abandoned his Lady the Dutchess; and that every body blamed her for it, as no doubt she deserved to be, insomuch that there was nothing but that one consideration, she was obliged to tell him, that he must resolve to break up with her, since their converse was equally shameful, and sinful to them both.
— Marie Catherine de la Motte (trans.), Memoirs of the Court of France, 1702
Oddly enough, this sense appears to have seen little to no use for almost two centuries following, and did not enter into common use until the end of the 19th century.