Making good on a promise made 20 months ago, officials of Seattle-based Washington Mutual Inc. have signed an agreement to purchase United Western Financial Group Inc. and its two subsidiaries, United Savings Bank and Western Mortgage Loan, for $80.3 million in cash.

The purchase will help Washington Mutual be one of the leading mortgage lenders in Utah.Kerry Killinger, Washington Mutual chairman, president and chief executive officer, said when the company entered the Utah market in February 1995 the intention was to be the state's No. 1 mortgage lender and Utahns' top choice for consumer-oriented financial products and services.

"This acquisition will place us in a strong position to achieve that goal," he said.

"This transaction will join two great consumer banks and will result in one of the leading mortgage lending operations along the Wasatch Front, said John B. Goddard, chairman of United Western.

The transaction requires the approval of banking regulators and a majority of shareholders of United Western's common stock. Pending the approval, the sale is expected to be completed in the last quarter of 1996.

Earlier this year, Washington Mutual signed a merger agreement with Ogden-based Utah Federal Savings Bank, a move that should be completed later this year.

Washington Mutual operates 16 full-service financial centers and a loan center in Utah. United Savings Bank operates nine branches, seven of which are in the Salt Lake area, and one in St. George and Idaho Falls, Idaho.

Western Mortgage Loan operates two loan offices in Salt Lake City; one in Portland, Ore.; one in Boise; one in Las Vegas; and one in Reno, Nev. It also operates a loan office in Missoula, Mont., under the United Western name. In addition to originating residential mortgages, the company services more than $4.3 billion in loans, including $3.5 billion in which its owns the servicing rights.