Late on Sunday night the deal was sealed for $236 million after the US central bank announced it would provide a $30 billion cash injection to facilitate the deal.
The investment bank and brokerage's shares closed down 47 per cent after rumours of the takeover began on Wall Street on Friday.
Jamie Dimon, JPMorgan Chase's chairman and chief executive, was quoted by AFP as saying: "Bear Stearns' clients and counterparties should feel secure that JPMorgan is guaranteeing Bear Stearns' counterparty risk. We welcome their clients, counterparties and employees to our firm, and we are glad to be their partner."
Although the move was supposed to instil confidence in markets, especially with the fact that the government decided to help out to stop the bank going under, it has actually sparked widespread worry.
In Tokyo the Nikkei 200 fell one per cent on opening this Monday and prices continued to drop, falling to a 31-month low at the time of writing.
In early trading the FTSE 100 also fell by two per cent in London and worse is expected to follow.