The United States, will establish full diplomatic relations with the People's Republic of China on Jan. 1, President Carter announced last night.

In ending three decades of hostility between Washington and Peking, the United States will cut its longstanding diplomatic and military ties with Taiwan, the president announced.

Carter said Chinese Vice Premier Teng Hsiao-ping will visit Washington at the end of next month and that there will be an exchange of ambassadors between the United States and the People's Republic on March 1.

Remaining U.S. military personnel on Taiwan, which number about 750, will be pulled out within four months of the normalization of U.S. relations with Peking.

The historic development, the culmination of a process that began under President Richard M. Nixon, and continued under his successor, Gerald R. Ford, reached an unexpectedly rapid conclusion within the last two weeks.

The announcement came in a joint communique issued by the American and Chinese governments and in a nationally televised address to the nation by Carter.

"We do not undertake this important step for transient tactical or expedient reasons," the president said in his speech form the Oval Office. "It recognizes that the government of the People's Republic is the single government of China. We are recognizing simple reality."

Normalization of diplomatic relations with Peking along with the increased commercial and cultural contacts it will bring, "will contribute to the well-being of our nation and will enhance stability in Asia," Carter said.

The president paid passing tribute ot Taiwan into which the United States has poured billions of dollars in military and economic aid since Mao Tse-tung overthrew the government of Chiang Kai-shek in 1949.

"We will continue to have an interest in the peaceful resolution of the Taiwan issue," Carter said. I have said special attention to ensuring that normalization of the relations between the United States and the People's Republic will not jeopardize the well-being of the people of Taiwan."

There was no elaboration in the speech or communique on what assurances the Chinese government has provided to the United States concerning Taiwan's security. Administration officials who briefed reporters following the speech provided lttle additional information on that point.

The officials noted that in a separte, unilateral statement also issued last night, the U.S. government declared its confidence that the people of Taiwan "face a peaceful and prosperous future" and that it expects that the Taiwan issue will be settled peacefully by the Chinese themselves."

The officials also noted recent public statements by Chinese leaders that the Chinese " are a patient people." But when pressed, the administration officals did not cite any specific assurances on the security of Taiwan that were provided the United States by China as part of the normalization agreement.

Under terms of the mutual defense treaty between the United States and Taiwan, formal military ties between the two countries will end at the end of 1979, following a provision for a one-year notice before the pact can be terminated.

During that time, U.S. officials said, the United States will continue to deliver military equipment already contracted for by Taiwan. Moreover, the officials said, even after formal military ties end, the United States will continue to make available to Taiwan "selected defensive weaponry" on a "restrained basis."

The Nationalist Chinese government reacted rapidly and angrily to the commique, issuing a strongly worded statement that condemned the United States and reasserted its long-term goal of regaining mainland China.

The U.S. action, Premier Chiang Ching-Juo said in a statement from Taipei, "has not only seriously damaged the rights and interests of the government and people of the Republic of China, but also has a tremendous adverse impact upon the entire free world."

"Viewed from whatever aspects, the move by the United States constitutes a great setback to human freedom and a emocratic institutions. It will be condemned by all freedom-loving and peace-loving people over the world."

The United States, the premier said, had given repeated assurances to maintain diplomatic relations with his government. "Now that it has broken the assurances," he said, "the United States government cannot be expected to have the confidence of any free nations in the future."

The statement was drawn up in an emergency early morning meeting in Taipei.

The government's embassy here was informed of the communique early last night when minister Tai-chu Chen, acting in behalf of Ambassador James C. H. Shen, who was in Arizona, was called to the State Department for a meeting with Deputy Secretary of State Warren M. Christopher.

The agreement announced last night by the president was reached yesterday after a sequence of unpublicized neotiations in Washington and Peking. There were seven negotiating sessions, starting last June, between U.S. envoy Leonard Woodcock and Chinese officials in Peking. In addition, Carter met twice in Washington with Officials of the Chinese liaison office here.

U.S. officials cited as a key point in this process a meeting the president had Sept. 19 with Chai Tse-min, head of the Chinese liaison office here, during which Carter set out the U.S. terms for normalization of relations.

There was no announcement last night of who will be the American ambassador to Peking. Speculation centered on Energy Secretary James R. Schlesinger, but administration officials at the White House strongly suggested that Woodcock would remain in Peking as ambassador after March 1.

In announcing the decision and in talking with reporters later at the White House, the president paid tribute to his Republican predecessors, Nixon and Ford, for starting the diplomatic process that culminated in last night's developments.

The Carter decision was denounced in vehement terms by conservative Republicans, but it drew the backing of Ford and most major Democrats. The president described the congressional reaction as "mixed" and said he was not suprised by it.

Congressional leaders were briefed on the decision by Carter three hours before the televised speech. It was part of a day of intense speculation and mounting tension at the White House that included an extraordinary briefing before the speech for network television anchormen, who were called to Washington from New York.

Following the speech, Carter, obviously pleased, appeared unexpectedly in the White House press briefing room in the midst of a "background" briefing on the developments.

Calling it "an extremely important moment," the president predicted that U.S. relations with China would not affect the strategic arms limitation treaty (SALT) talks with the Soviet Union, which are nearing a conclusion.

"The Soviets know we have no desire to use our new relations with the People's Republic to the disadvantage of the Soviets or others," he said. "This will enhance stability."

Carter said the Soviets had been anticipating such a move by the United States and "were not surprised" when Soviet Ambassador Anatoliy F. Dobrynin was informed of it yesterday afternoon by National Security Affairs Adviser Zbigniew Brzezinski.

Conceding that the development will not be met with "massive applause" on Taiwan, Carter said its interests will be "adequately protected" under the new arrangement and stressed that the United States will continue commercial, cultural and other ties with Taiwan through nongovernment channels.

Administration officials said that to maintain close ties with Taiwan, legislation will be introduced next year that would grant it some of the advantages now afforded only to nations with which the United States has full diplomatic relations. These advantages include eligibility for loans from the Export-Import Bank.

There was a simultaneous announcement of the developments in Peking this morning.

The communique issued by the two governments said the United States "acknowledges the chinese position that there is but one China and Taiwan is part of China" and that the communist government in Peking is "the sole legal government of China."

"Within this context," the communique added, "the people of the United States will maintain cultural, commercial and other unofficial relations with the people of Taiwan.

In many respects the relationship outlined last night between the United States and Taiwan resembles the one negotiated between Japan and Taiwan. Washington has been putting as much distance as possible between itself and Taiwan since the 1972 Shanghai communique, which committed the United States to a "normalization" of its relations with mainland China.

The president's speech last night was unusally brief-just over 10 minutes. He began by reading the text of the joint communique and said closer ties with China "can bebefically affect the world in which we and our children will live."

"Before the sttrangement of recent decades, the American and Chinese people had a long history of friendship8" Carter said. "We have already begun to rebuild some of those previous ties. Now, our rapidly expanding relationship requires the kind of structures that diplomatic relations will make possible."