Agriculture Secretary John R. Block, a controversial lightning rod who presided over some of the toughest times for U.S. farmers since the Great Depression, announced yesterday that he will leave the administration next month for a job in private business.

Block, a West Point-educated hog farmer and member of President Reagan's original Cabinet, said his chief aim of shepherding a new farm bill through Congress had been achieved and that "today, now, is the time to leave."

Block, 50, said he would remain at his post until mid-February. He said he is considering several job possibilities but would not return to farming in Illinois, where his son runs the family operation.

The secretary, who for months had denied any intention of resigning, said he would offer President Reagan his ideas on a successor. Block predicted that Reagan would decide quickly to provide continuity in administration of the new "market-oriented" farm bill signed by the president three weeks ago.

Washington speculation has centered on, among others, Richard E. Lyng, deputy secretary of agriculture until last year; Lyng's successor, California-Arizona farmer John R. Norton; Clayton Yeutter, special trade representative for the White House; Richard Bell, a rice-industry official with previous government service, and Robert Delano, a Virginia farmer who heads the American Farm Bureau Federation.

Reagan, asked at his news conference last night whether he would seek another working farmer to succeed Block, said he wanted someone with similar qualifications. The president also said he agreed with Block's assessment that the farm economy has bottomed out. "I think we have," Reagan said. But he warned that it would take "a little patience" before farmers begin to recover significantly.

Block, with his wife at his side, said at a news conference yesterday he believes that he has "made a difference" as secretary, and that U.S. agriculture is "starting to turn the corner" from stress that has bankrupted thousands of farmers and driven farm exports to their lowest level since 1981.

He said the new farm bill, a congressionally ordered reorganization of the Farm Credit System and the Gramm-Rudman-Hollings budget-balancing legislation will be factors in improving farm prices, stabilizing land values and boosting exports.

But agriculture's recent woes have left Block with several distinctions: Federal farm spending reached record highs during his tenure, his 1983 surplus giveaway (PIK) program was the largest cropland idling program in history and he was criticized almost constantly as an evangel of unpopular administration policies on farm subsidies and credit assistance.

Block responded to critics infrequently but noted yesterday the "frustration" of overseeing and ministering to the problems of an industry "that tended to be out of the reach of the secretary."

Although personally popular among members of Congress and farm leaders, Block was increasingly chided by them for his unrelenting optimism about an economic turnaround in agriculture that has not come. Block resolutely defended Reagan's farm policies and rarely, even off-the-record, would he discuss bickering or dissension within the administration.

Block provoked more criticism and a shower of unhappy publicity in 1983 when he and his family spent a week on a food-stamp budget of $58 and then pronounced the diet "quite adequate." The move came as the administration was attempting to cut the food-stamp program, which Block administered.

But as economic stress mounted across the Farm Belt during the last two years, the political criticism escalated. By last fall, Republicans such as Rep. Edward R. Madigan, from Block's home state, were publicly decrying Block's apparent inability to win more White House sympathy for farm problems. Others called for his resignation.

Ironically, however, most observers gave Block credit for elevating farm problems to attention at the Cabinet level and for pressuring the White House to lift former president Jimmy Carter's partial embargo on grain sales to the Soviet Union, initiated in response to the Soviet invasion of Afghanistan in December 1979.

At his news conference yesterday, Block listed ending the embargo in 1981 as one of his main accomplishments as secretary. "That was the first big battle in the administration," he said. Since then, the Soviets have returned to the U.S. market as major buyers of farm goods.

Another irony of Block's tenure was that his private farming operations, left in the hands of his son and father when he came here in 1981, suffered from much of the same economic tumult that has driven others out of farming at a rate unmatched since the gloom of the 1930s.

High interest rates, declining farm prices and plummeting land values in the Midwest put the Block farm under severe pressure and led to the breakup of several other farming ventures in which he and partners were heavily leveraged.

A Farmers Home Administration loan two years ago to one of the partners raised controversy, although Block denied any role in obtaining the loan.

Block told reporters parenthetically yesterday that his financial situation has improved during the last year because he, like other stressed farmers, "had to make adjustments" to keep his operation afloat.

He said he would leave his son, Hans, in charge of the farm. "I don't think I would be an asset to him on a full-time basis. He doesn't need a boss," he said.

Although Block denied as recently as Monday that he intended to resign, he said he decided last fall that he would leave the administration after the rigorous farm-bill debate.

"I set the farm bill as my goal and objective," he said. "My objective was to carry the mail for the president."

Reacting to Block's resignation statement, House Agriculture Committee Chairman E (Kika) de la Garza (D-Tex.) mirrored congressional sentiment:

"The differences between Congress and the administration on farm policies are philosophical and that is not going to change. But if you're going to have these differences, it might as well be with someone who is personally kind and considerate -- and John Block has been that."

John Lewis of the Farm Bureau added: "Any failure he had was the result of one of the most horrendous times in agricultural history."