President Reagan will nominate Adm. William J. Crowe Jr., currently Pacific commander, to become chairman of the Joint Chiefs of Staff, Pentagon sources said yesterday. If confirmed by the Senate, Crowe will replace Army Gen. John W. Vessey Jr. on Oct. 1, more than eight months before Vessey's four-year term is to expire.

The announcement is expected today.

Vessey has been telling friends for some time that he would like to retire early. He will be doing so at a time when the chairman of the Joint Chiefs will be presiding over the most contentious apportionment of the Pentagon budget since President Reagan took office, because of congressionally imposed cuts in the rearmament program.

Vessey and Crowe are a study in contrasts. Vessey, 63, is a rough-hewn former mud soldier who received a World War II battlefield commission in Italy, while Crowe, 60, is a polished diplomat-officer who earned a doctorate in political science from Princeton after graduating from the U.S. Naval Academy in 1946.

Crowe, as commander in chief of Pacific and Indian Ocean forces, currently heads the largest of the unified commands. He is responsible for Army, Navy, Air Force and Marine activities in an area covering about half the globe and negotiates with dozens of governments as part of his job.

Pentagon sources said that Defense Secretary Caspar W. Weinberger was immensely impressed by Crowe's knowledge of world affairs, and had recommended him to Reagan when it became obvious that Vessey wanted to retire rather than accept an extension of his four-year term, which would expire June 18.

The other leading candidate to replace Vessey was Adm. James D. Watkins, 58, chief of naval operations, the sources said. Watkins' current tour expires in June.

Crowe's associates predict that he will be more innovative as chairman than was Vessey, who had a low-profile, low-key style. Vessey opposed changing the Joint Chiefs, as recommended by his immediate predecessor, Air Force Gen. David C. Jones, who thought the organization lacked effectiveness and accountability.

The Joint Chiefs chairman is the highest-ranking military adviser to the president and the overseer of the corporate body of the chiefs, comprised of the heads of the Army, Navy, Air Force and Marine Corps. The chairman presides when military issues are thrashed out by the chiefs and presents the corporate view to the president.

Crowe has a reputation as a skillful negotiator both within the Pentagon and abroad.

After submarine duty and service in Vietnam as an adviser to South Vietnamese riverine forces, Crowe was promoted to rear admiral in 1974. He became deputy director of Navy planning and went on to the Pentagon's "Little State Department," the International Security Affairs Office, specializing in East Asia and the Pacific.

His recent assignments included commander of the Middle East Force, with headquarters in Bahrain; deputy chief of naval operations for planning and operations, and commander of allied forces in southern Europe. Crowe is renowned as a raconteur with a seemingly unlimited supply of humorous stories that have lit up shipboard wardrooms and drawing rooms ashore.

Crowe has said that the United States and the Soviet Union are "engaged in a monumental mistrust of each other" but "somehow must find a way to coexist . . . peacefully."

In the meantime, he said, "we need desperately to modernize our weapons delivery systems. I don't suggest that we increase our arsenal of warheads, only that we modernize our delivery systems so that we can continue to meet the Soviet threat" and convince Moscow that "it's in our mutual best interest to disarm."

Crowe is among those military leaders who believe that any war with the Soviet Union would escalate to a worldwide conflict rather than be confined to one area of the world, such as a war only at sea.

As new chairman, Crowe would almost certainly be asked to take a fresh look at military plans for preempting terrorists acts or retaliating for them.