The United States yesterday reached agreement with the final holdout group of Micronesian islanders on a permanent new relationship, presaging the end of the 33-year-old U.S. trusteeship over a vast region of the mid-Pacific.

A formal governmental compact with the United States, the result of 12 years of off-and-on negotiations, is scheduled to be initialed at the State Department at noon tomorrow by representatives of the Republic of Palau, a newly established ministate in the western end of the Caroline Islands. Two similar new ministates, the Marshall Islands and the Federated States of Micronesia, initialed the same compact Oct. 31.

Several days of down-to-the-wire negotiations in Washington ended late yesterday with a decision by the Palauan negotiators to accept the latest version of the U.S. offer. Carlos Salii, chairman of the Palau status committee, said the final decision to initial the proposed compact came at 6:30 p.m. after all-day meetings among about 20 island representatives.

Micronesia, a watery empire of more than 2,000 small islands, has been administered by the United States as a strategic trusteeship of the United Nations since 1947, shortly after the Japanese were ousted from the area in some of the bloodiest battles of World War II. As other powers gave independence to their official wards, Micronesia became the last international colony under United Nations auspices and, as such, a growing embarrassment to the United States.

The long negotiations for a permanent self-governing status, which began in 1969, were complicated by divisions and fragmentation among the far-flung islanders, bureauratic bickering among Washington agencies and the revelation in 1976 that the Central Intelligence Agency had bugged the Micronesian negotiating team at an earlier stage of the talks.

The Ford administration agreed on terms that split off the Northern Marianas, in the far western reaches of Micronesia, as a separate commonwealth. While this solved a small part of the problem, this development created a more serious problem of common agreement in the rest of the vast area.

The Carter administration's push for a settlement, led by chief U.S. negotiator Peter Rosenblatt, began late in 1977 with a presidential commitment to terminate U.N. trusteeship by 1981. Several procedural steps remain, such as formal signing of the compact by all the parties, ratification by legislatures and a United Nations-sponsored plebiscite, but the initialing of the document is considered a giant step toward Carter's goal.

The mid-Pacific empire, long viewed in Washington as of strategic importance, is the site of the U.S. missile testing grounds at Kwajalein in the Marshalls. The U.S. military is interested in establishing a military presence in the Palau islands. But the greatest U.S. strategic stake, in the view of many officials, is simply in keeping unfriendly navies out of the area and thus heading off a potential threat to Hawaii, Guam and other Pacific points.

Palau, the Marshalls and the Federated States (which ranges over the thousands of miles between the other two) will each be separate nations under the new compact, responsible for their own government and internal affairs but with control over military and defense affairs in the hands of the United States. The United States will have the obligation to defend them, and the option to keep others out.

One hangup in negotiations with Palau was a provision in that island group's 1979 constitution barring nuclear weapons from its territory. A side agreement, which must be approved by a two-thirds vote of the islanders, has been drawn up to override this provision, permitting normal development in the area by U.S. nuclear armed military forces and nuclear-powered ships.

The military arrangements are binding for 15 years and are subject to renewal after that, if both sides agree.

In return for the U.S. military rights, the Microesian states have been promised grants averaging about $100 million yearly for 15 years, divided among the three ministates. In addition, the new states will continue to benefit from some programs available to U.S. citizens.

The three nations will have their own flags, passports and the panoply of independence in an arrangement that is called "free association" with the United States. All together, a little more than 100,000 persons will inhabit the three new states of the Pacific.