The Federal Reserve Bank of New York, in a statement Monday, confirmed its role in the arrangement.

“We believe the amended terms are fair to all sides and reflect the value and risks of the Bear Stearns franchise,” the chief executive of JPMorgan, Jamie Dimon, said in a statement, “and bring more certainty for our respective shareholders, clients, and the marketplace. We look forward to a prompt closing and being able to operate as one company.”

In the same statement, the chief executive of Bear Stearns, Alan D. Schwartz, said: “Our board of directors believes that the amended terms provide both significantly greater value to our shareholders, many of whom are Bear Stearns employees, and enhanced coverage and certainty for our customers, counterparties, and lenders.”

“The substantial share issuance to JPMorgan Chase was a necessary condition to obtain the full set of amended terms, which in turn, were essential to maintaining Bear Stearns’ financial stability,” Mr. Schwartz said.

While the rules of the New York Stock Exchange generally require shareholder approval before a company issues securities that are convertible into more than 20 percent of the outstanding shares, an exception is permitted in cases where a delay would jeopardize the viability of the company. Under a Delaware precedent, where the companies are incorporated, a company can sell up to 40 percent without shareholder approval.

The new deal could raise even more questions about the Fed’s involvement in the negotiations. The central bank had directed JPMorgan to pay no more than $2 a share for Bear to assure that it would not appear that the Bear shareholders were being rescued, people involved in the negotiations said Sunday night.

Image The headquarters of Bear Stearns in Midtown Manhattan. JPMorgan Chase initially offered $2 a share for Bear, angering the beleaguered firms stockholders who said the offer was too low. Credit... Patrick Andrade for The New York Times

A spokesman for the Federal Reserve would not comment on the central bank’s involvement in the negotiations and denied that it had directed the original sale price.