It was not known whether Malpass and Ryding have accepted positions at another company, according to the source.
Malpass and Ryding declined to comment. JPMorgan also declined to comment.
In April, JPMorgan had said that Bruce Kasman remained its chief economist.
Both Malpass and Ryding have been with Bear since the early 1990s. In 2001, Malpass was named the firm's chief global economist and Ryding chief market economist, after the retirement of then-Chief Economist Wayne Angell, a former Federal Reserve Governor.
Before joining Bear, Malpass held a series of top economic positions in the Reagan and Bush administrations, while Ryding was an economist at the Federal Reserve Bank of New York and the Bank of England.
On Thursday, Bear Stearns shareholders approved a plan to sell the company to JPMorgan for less than $10 a share. The deal is expected to close on Friday.
Roughly 6,500 of the 14,000 Bear Stearns' employees are expected to join J.P. Morgan.
In March, Bear, which had been the No. 5 U.S. investment bank, was at the brink of collapse due to hefty losses tied to exposure to bad mortgage loans.