Bailouts and other measures employed to keep the euro area intact "will lead to not only an economic but a political crisis", according to King's new book, The End of Alchemy, which is being serialised in the Daily Telegraph.
"Put bluntly, monetary union has created a conflict between a centralised elite on the one hand, and the forces of democracy at the national level on the other," says King.
"This is extraordinarily dangerous."
King says that it would have been possible to divide the Eurozone into two separate areas in 2012, "when concern about sovereign debt in several periphery countries was at its height". He says some members could have been temporarily relegated to a "second division", with the aim of being promoted back into the first division after a period of time.
However, he adds: "It may be too late for that now. The underlying differences among countries and the political costs of accepting defeat have become too great."
King highlights Germany as facing a "terrible choice", and warns that German voters may come to resent the "losses imposed on them by the need to support their weaker brethren".
"Undoubtedly the easiest way to divide the euro area would be for Germany itself to exit," he says.
"But the more likely cause of a break- up of the euro area is that voters in the south will tire of the grinding and relentless burden of mass unemployment and the emigration of talented young people."
King was governor of the Bank of England from 2003 to 2013, overseeing the central bank throughout the global financial crisis.