President Reagan yesterday nominated Clayton Yeutter, president and chief executive of the Chicago Mercantile Exchange and a veteran of trade and agriculture posts in the Nixon and Ford administrations, to be United States trade representative.

Yeutter, 54, replaces William Brock, Reagan's nominee to be Labor secretary.

He accepted the job after a session with the president in the Oval Office. Yeutter comes to the administration at a time characterized by strained relations with Japan, a surge of protectionist sentiment in Congress and a record U.S. trade deficit.

White House spokesman Larry Speakes said he was "as good a replacement as could be found" for Brock and was selected from more than 30 candidates.

Yeutter served as deputy special trade representative from 1975 to 1977 during the Ford administration. He was a strong contender for the post of Agriculture secretary in the first Reagan term, but was passed over for John R. Block because of reported opposition at the time from Sen. Robert Dole (R-Kan.), now Senate majority leader.

A White House official said yesterday that Dole approved the choice this time. The position of U.S. trade representative carries Cabinet rank, and Yeutter will attend National Security Council meetings "as appropriate," another official said.

Senate Republican sources said, however, that the choice was not universally welcomed on the Finance Committee and that its chairman, Robert Packwood (R-Ore.), was not consulted or informed in advance.

Others applauded the choice. "His task is extremely difficult, but he is up to it," said Michael Samuels, a vice president of the U.S. Chamber of Commerce. "As chairman of the U.S. chamber's European-U.S. agribusiness council, he reflected honestly and frankly the problems faced by American agricultural interests and worked constructively with his European counterparts."

American Textile Manufacturers Institute President James H. Martin Jr. said in a statement that Yeutter's background and experience "give him a realistic view of the serious trade problems the nation is facing."

Speakes noted that the Chicago Mercantile Exchange is the nation's top trading market for foreign currencies. He said that, when Yeutter was at the trade office in the 1970s, he handled a number of negotiations, including one dealing with the so-called "cheese war" in which European nations withdrew subsidies to cheese makers, and talks on textiles and steel.

Yeutter has been president and chief executive of the Chicago exchange since 1978. Previously he was a senior partner in the law firm of Nelson, Harding, Yeutter & Leonard in Lincoln, Neb.

He served as deputy special trade representative from 1975 to 1977. Prior to that he served as assistant Agriculture secretary for international affairs and commodity programs (1974-75), assistant secretary for marketing and consumer services (1973-74), and Consumer & Marketing Service administrator (1970-71).

He was director of the University of Nebraska Mission in Columbia from 1968 to 1970 and executive assistant to the Nebraska governor from 1966 to 1968. He was a faculty member in the Department of Agricultural Economics at the University of Nebraska from 1960 to 1966.

From 1957 to 1975, he operated a 2,500-acre farming, ranching and cattle-feeding enterprise in central Nebraska, the White House said.

He is a member of the boards of ConAgra Inc., the U.S. Meat Export Federation, the Japan America Society of Chicago Inc. and the Chicago-Tokyo Bank.