I don't know if this has anything to do with the seemingly widespread acceptance of the idea of soulmates, but Plato addressed this in The Symposium.
A quote from my introductory philosophy textbook:
"Asked to tell his fellow dinner guests about the nature and origins of love, the playwright Aristophanes invents a wonderful fable, in which we were all long ago 'double creatures,' with two heads, four arms, four legs, and enormous intelligence and arrogance (or what the Greeks called hubris). To teach humans a lesson, Zeus, the king of the gods, struck the creatures down and cleft them in two- 'like an apple,' Aristophanes says- so that each resulting half-person now had to walk around the world, looking for his or her 'other half.'"
.......and a quote from The Symposium itself:
"And so, when a person meets the half that is his very own,........then something wonderful happens: the two are struck from their senses by love, by a sense of belonging to one another, and by desire, and they don't want to be separated from one another, not even for a moment."