J.P. Morgan Chase & Co.'s penalties for the "London whale" trading fiasco are expected to total $500 million to $600 million as part of a far-reaching settlement that could wrap up as soon as next month, according to people close to the situation.

The Justice Department, Securities and Exchange Commission, Commodity Futures Trading Commission, Office of the Comptroller of the Currency and the U.K's Financial Conduct Authority are conducting investigations into J.P. Morgan's handling of the episode. Not all agencies...