NEW YORK (AP) _ National Westminster Bank USA and First Jersey National Corp. announced today an agreement to merge in a cash transaction they valued at about $820 million.

NatWest, the U.S. subsidiary of Britain's giant National Westminster Bank PLC, said it had a definitive agreement to pay $82 cash for each of First Jersey's 7.6 million common shares.

The agreement also would give First Jersey National's preferred shareholders the right to receive $82 for each of their shares.

First Jersey National, which is based in Jersey City, also gave NatWest the option to purchase newly issued shares equaling 24.9 percent of the company's common shares on a pro forma basis.

If approved by shareholders and banking regulators, the merger would create a bank holding company with about $15.8 billion in assets operating 250 branches in New Jersey, New York City and the New York metropolitan area.

Officials said they expected to complete the merger shortly after Jan. 1, the effective date of New Jersey's interstate banking law.

The merger marks the latest in a recent series of major bank mergers in the East, headed by last week's announcement of a $1.34 billion deal between First Fidelity Bancorporation of Newark, N.J. and Fidelcor Inc. of Philadelphia. Also last week, PNC Financial Corp. of Pittsburgh and Central Bancorporation of Cincinnati said they would merge in a deal valued at about $700 million.

Merger rumors surrounding First Jersey National had pushed its stock up by $9 to $64 in the national over-the-counter market Tuesday before trading was halted pending an announcement. The stock jumped to $76.50 a share in early trading today.

William T. Knowles, NatWest USA's chairman and chief executive officer, will assume those roles with the bank holding company formed in the merger, which will be a subsidiary of NatWest PLC.

''This is a welcome extension into a contiguous market of our successful NatWest USA banking operations in New York,'' Tom Frost, NatWest group chief executive, stated in London. ''New Jersey has one of the highest growth rates in the United States, and the acquisition of this first class, well-managed bank, operating in areas compatible with our New York business, will bring significant benefits to both banks and to the NatWest Group in general.

NatWest PLC, which acquired its U.S. subsidiary in 1979, has consolidated assets of about $140 billion, with 3,900 offices and 96,000 employees worldwide.

NatWest USA has assets of $11.4 billion, and First Jersey National has assets of $4.4 billion.