Black and white Rhodesian leaders reached agreement yesterday that Prime Minister Ian Smith will remain as the titular head of an interim government that will rule this country until the advent of full black majority rule Dec. 31, informed sources said.

Smith and three black leaders --Bishop Abel Muzorewa, the Rev. Nda-baningi Sithole and Chief Jeremiah Chirau -- agreed that they would comprise a four-man executive council that would head the Rhodesian government during the transition period.

Informed sources said Smith would retain the title of Prime Minister, but that the real power would be wielded by the executive council.

Emerging from a three-hour bargaining session with leaders of the black delegations, Smith said a formal agreement would be signed this morning following a plenary session of the constitutional conference that has been under way here since early December.

None of the four would discuss details of the compromise apparently reached over several key points that had been holding up a settlement.

Chief among these was the issue of whether Smith would remain as prime minister, and whether te present white-dominated Parliament would continue to function until the new black majority government formally takes over at the end of the year.

Wednesday, Smith told a London newspaper that he was remaining as prime minister and it was believed here last night that the compromise involves a temporary dual form of government with real power invested in the proposed executive council made up of the four heads of delegations.

Announcement of the accord yesterday came only 15 days after the four parties to the internal settlement talks came to an accord on eight basic principles that are to underline a new constitution providing for black majority rule and safeguards for the 270,000 whites living in Rhodesia.

The four parties were understood to be in a hurry to sign an agreement on the interim government before Bishop Muzorewa, who heads the United African National Council (UANC), leaves this coming weekend for crucial talks in London with British Foreign Secretary David Owen.

The other key factor in the signing of an agreement here this week is the debate scheduled to get underway Monday in the United Nations Security Council on the whole Rhodesian internal settlement talks.

The agreement will now present both the British and American governments, as well as the United Nations, with a falt accompli, and thus force them to choose between support for the internal settlement or the rival Anglo-American proposals for resolving the Rhodesian constitutional dispute.

The British and Americans have been negotiating separately with the Patriotic Front, the guerrilla alliance based outside Rhodesia and regarded as the arch-enemy of the internal black and white leaders.

But in the past two weeks, both the British and Americans governments have been hinting they may be prepared to recognize an internal agreement, provided certain conditions are fulfilled, and to drop their support for the Patriotic Front.

In any case, the agreement that is to be signed here today is certain to touch off a furious diplomatic battle with both the United Nations and the Organization of African Unity over the legitimacy of the new multiracial interim government that is to be established here within weeks.

The announcement yesterday that an agreement had finally been reached came as something of a surprise as only a few hours earlier, government officials were extremely pessimistic that a breakthrough was in the offing.

Wednesday, the four leaders, meeting alone again for three hours without their delegations, were reported to have agreed on a rotating chairmanship for the executive council that is charged with preparation of a consistitution and organization of elections on the basis of universal adult suffrage.

They also set Dec. 31 as the target date for turning over full authority to an elected black majority government.

This left still to be resolved at yesterday's session the issues of whether the present Parliament would continue to sit at least until new elections are held, and whether Smith would thus remain as prime minister even while serving simultaneously in the executive council.

The third issue to be decided was the make up of the ministerial council, a body being set up under the executive council to run the country during the transitional period.

Smith had been arguing that the present Parliament, which is dominated by his Rhodesia Front Party, would have to remain in existence to pass enabling legislation allowing the interim government to be established.

Since Smith is constitutionally prime minister of the present Parliament, he would have to continue to hold that position until it is dissolved.

At the same time, he has been pressing for a broadly based ministerial council consisting of co-ministers, one black and one white, for each portfolio.

The black delegations, Bishop Muzorewa's UANC in particular, had been demanding that both Smith and Rhodesia's largely ceremonial president resign immediately, and that the executive council, where blacks will hold a three-to-one majority, rule in their place. At the same time, the present Parliament would immediately be disbanded.

The black delegations also wanted equal representation for all four delegations on the ministerial council, thus giving them again a three-quarters majority on that body.

The compromise that was being suggested Wednesday was to allow the present Parliament to remain in existence, with Smith as its lame-duck prime minister.