Yigael Yadin's moderate reform party, the Democratic Movement for Change, voted tonight to join the Likud-led government of Menachem Begin, greatly strenthening Begin's majority in Parliament.

Begin's government had held only a slender, three-voted majority in the 120-member Knesset, or Parliament. It will now have 18.

"Now we shall appear before the world as a stable government," the prime minister was quoted as saying, "and we shall be able to stand firm."

The vote at the meeting of the Democratic Movement's central council in Tel Aviv was 68 to 42, climaxing nearly six hours of bitter debate. Observers said Yadin's persuasive arguments in favor of joining the government decided the issue.

Although Begin pledged, "We shall work in full harmony," it is too early to say how much real power the Democratic Movement may be given in influencing government policy. But the significance of its decision tonight goes far beyond the addition of 15 seats to Begin's parlimentary majority.

The Democratic Movement agrees with Likud on what has become the "Three no's of Israeli policy: no negotiations with the Palestinian Liberation Organization, no Palestinian state and no withdrawal to 1967 frontiers. Unlike Likud, however, the Democratic Movement is not totally opposed to territorial concessions on the West Bank and in Gaza and opposes the present government's policy of extending Jewish settlements into the midst of the Arab population on the West Bank.

Domestically, Begin now is freed from over-dependence on the small, orthodox, right-wing religious parties that threatened so much trouble with their demands to impose their beliefs on secular Jews. He also is freed from his dependence on the Gush Emjnim (Faith Bloc) movement, whose desire to push settlements into the Arab heartlands on the West Bank bordered on the fanatic, in the view of many Israelis.

Yet Begin is still in favor of these settlements, although he has tried to limit them to please the Americans for the time being, and it is uncertain how effective the Democratic Movement can be in blocking future settlements.

The Democratic Movement brings into the government a number of men with badly needed managerial skills.

"The trouble with Begin's first four months in office, as fas as domestic politics is concerned, has been that there is only one Snow White and all the rest are dwarfs," said a prominent political commentator who supports the Democratic Movement.

Twice, the Democratic Movement earlier broke off coalition negotiations with Likud because Yadin and others felt that to join the government would be to compromise principles. But Likud's proven flexibility on procedural matters involving Geneva obviously impressed Yadin. But perhaps the most important factor in Yadin's change of heart was a 12-day trip to the United States, from which he returned two days ago.

Yadin told the Democratic Movement's council he had become convinced that patriotic considerations must be placed above party interest. The Soviet-American officials including Secretary of State Cyrus R. Vance and Zbigniew Brzezinski, President Carter's national security adviser, had convinced him that a dangerous confrontation with the United States was in the making and the time had come to put political differences aside in the cause of national unity.

Yadin, Israel's chief of staff in the 1948 war said political leadership that remains insensitive to changing situations is as bad as military leadership that rushes into battle with elaborate plans without updating and overhauling them to meet changing battle conditions. He also said that although the Democratic Movement could support the government on most of its foreign policy, it would try to stop the West Bank settlements that have alienated Israel's friens abroad.

Another powerful factor in his decision, Yadin said, was American Jews who urged him to join the government. American Jews, although willing to support Begin against Arab of U.S. pressure, are not fully comfortable with Begin's government, he reported, and told him it would be easier to rally support in American if Yadin were in the government.

One important question is whether, as deputy prime minister, Yadin will automatically become acting prime minister, when Begin is absent. Begin's health is uncertain after a heart attack and two periods of hospitalization since May. Until now, Finance Minister Simcha Erhlich, the No. 2 man in Likud, has served as prime minister in Begin's absence. The Likud may not wish to relinquish that privilege, especially since it bears upon the matter of the succession to the prime minister's office. A decision is to be made by a government vote early next week.

Because Likud itself is a coalition of formerly independent parties, the presence of the Democratic Movement in the government may lead to new political configurations. The power of Begin's Herut faction, with 21 knesset seats, would be lessened, for example, should Likud's Liberal faction, headed by Simcha Errlich, join their 15 votes with the Democratic Movement's 15 on certain issues. The religious parties appear to be losers in the new government.

Under its agreement with Likud, the Democratic Movement will be allowed freedom of expression and freedom to abstain from voting on matters relating to the West Bank. Should the Democratic Movement demand it, the Knesset foreign affairs and defense committee will have the final say on settlements in the West Bank. This should have some effect on limiting these settements.

The Democratic Movement does not oppose Jewish settlements on the West Bank per se. But it agrees with the previous government that settlements should be located in sparsely populated regions for security reasons, not on top of Arab population centers to further the mystical concept of the land of Israel.