Israel's Cabinet voted today to implement the last stage in Israel's three-stage troop withdrawal from Lebanon and said that it will be complete by early June.

The 18-to-3 vote represented the government's final decision to end officially Israel's nearly three-year, direct involvement in Lebanon, which began with an invasion on June 6, 1982.

The exact timing of the final pullback was left vague in the statement issued at the end of today's Cabinet meeting, but Israeli officials have said publicly that they intend to have their troops out of Lebanon before the anniversary of the invasion. Privately, officials have said the withdrawal could be completed by the middle of May.

It is widely expected that the second stage of the withdrawal, authorized by the Cabinet on March 3, will take place this week, when Israeli troops pull out of positions they hold along Syrian lines in the mountains of eastern Lebanon. At the same time, the Israelis are expected to evacuate the port city of Tyre and the Lebanese Shiite Moslem villages in the mountains east of Tyre that have been the center of resistance to the Israeli occupation.

Reports from southern Lebanon today said Israeli units were destroying facilities and burning documents in apparent preparation for a rapid evacuation of the Tyre area.

Israeli officials said that by early May Israeli troops will be deployed in a so-called "security zone" north of Israel's border and that the final, third stage of the pullback to behind the international border will take place soon thereafter.

The depth of the security zone never has been defined by Israel, but officials said today that it will run from about five miles deep along the Mediterranean coast in the west to about 10 miles deep in the east. In this zone, village guards and the Christian-led South Lebanon Army, all supplied by Israel, will operate to keep the zone free of guerrillas.

However, as Defense Minister Yitzhak Rabin reiterated today, Israel will maintain "all freedom of military action" in the security zone and beyond if necessary. In effect, the situation along the border is expected to revert to what it was before the 1982 invasion, when Israeli units acting in support of pro-Israel Lebanese militiamen regularly patrolled the area north of the border.

Today's final withdrawal vote was opposed by three Cabinet ministers who are all former defense ministers.

Ariel Sharon of the right-wing Likud bloc, the architect of the invasion and now minister of industry and trade, reportedly argued that Israel should establish a 20-mile security zone and maintain a permanent Army presence in it.

Moshe Arens, a minister without portfolio from Likud, was said to have argued for an even deeper security zone or none at all.

Ezer Weizman, a minister without portfolio who is aligned with the Labor Party of Prime Minister Shimon Peres, reportedly urged a complete withdrawal without resort to security zone arrangements.

Foreign Minister Yitzhak Shamir, the Likud leader who opposed the three-stage withdrawal plan when it initially was approved in concept by the Cabinet in January, voted in favor of the final stage.

Following the Cabinet meeting, Rabin acknowledged to reporters that Israel had accelerated its withdrawal schedule in response to the wave of Lebanese Shiite attacks on Israeli troops in Lebanon. More than 20 Israeli soldiers have been killed in Lebanon since the first stage of the pullback was carried out on Feb. 16, speeding the final withdrawal schedule that originally was planned to be completed by early September.