The book you really want is M. Trundle, Greek Mercenaries from the Late Archaic Period to Alexander (Routledge, 2004). Trundle puts the transition in the early 4th century BCE. That doesn't mean there weren't any professional mercenaries prior to that date of course, but he highlights that period as the one where mercenaries started to be a significant social force as well as military -- you get large mercenary bodies floating around being not part of the populace. Earlier mercenaries were only auxiliary forces.

One reason he gives for the transformation is that in the 4th cent. there was simply too much warfare for citizen-farmer soldiers to keep up with it all. You can't be away at war 12 months of the year and expect your land to tend itself. Some specific wars helped establish the mercenary paradigm: you mention Xenophon's march of the ten thousand, but the 4th century saw Greek mercenary forces operating within Greece as well, notably in the Third Sacred War (350s and 340s): Phocis would never have been able to sustain a war against the Delphic amphictyony by itself, but by turning the wealth of Delphi into coins, they managed to sustain a 10-year war using primarily mercenary forces.