President Bush has picked outgoing federal drug policy director William J. Bennett as his surprise choice to become chairman of the Republican National Committee, Republican sources said last night.

Bennett, secretary of education in the Reagan administration, would take over the party chairmanship from Lee Atwater, who has been undergoing treatment for a cancerous brain tumor since last spring.

Atwater is expected to assume the title of "general chairman" in the shift of responsibilities. He will continue to advise Bush and the RNC while fighting the inoperable tumor.

Bush, who discussed the job with Bennett several times last week, will announce the decision after he returns next weekend from his trip to Europe and the Persian Gulf, Republican sources said.

The changes will take place officially at the RNC's winter meeting in January.

The outspoken and sometimes controversial Bennett will assume day-to-day control of a party that is badly divided in the wake of the federal budget fight and is struggling to find a new message to replace the anti-tax, anti-communism and antiabortion themes that have been eroded by events of the past 18 months.

Bennett's strong conservative credentials made him especially attractive to the White House, which has been trying to restore party unity since House Republicans broke with Bush over the effort to reduce the budget deficit and accused him of depriving the party of its most important message by abandoning his "no new taxes" pledge.

"Bennett is very good for the Republican base," a GOP source said in explaining Bush's choice.

Bush and other White House officials apparently believe Bennett has the ability to be a vigorous spokesman for the party in the ongoing debate with the Democrats, who increasingly see the president as vulnerable in 1992.

"He brings intellectual force, he brings a spokesman's quality to the job and he has great stature to lead the party," a Republican official said.

Many conservatives expected Bennett to speak out against some of Bush's policies, once he was freed from his responsibilities with the administration. Bennett's selection as RNC chairman will keep him on board as a defender and advocate for the president, sources said.

But one Republican said last night it was Bennett's loyalty to Bush during the fractious 1990 campaign that helped win him the job, the offer of which apparently caught even the self-confident Bennett by surprise.

"He was out there on the point politically," one Republican said. "He did a great deal of travel. He could have distanced himself. He didn't. He was vocal in support of the president during the end of the campaign."

White House and Republican Party officials have been wrestling with the question of how to restructure the RNC, both because of Atwater's illness and because of Bush's expected 1992 reelection bid. Others who had been under consideration for the RNC job included Commerce Secretary Robert A. Mosbacher, Bush's chief fund-raiser during the 1988 campaign, and Transportation Secretary Samuel K. Skinner, who has impressed party officials with his political skills as a Cabinet officer.

Atwater's illness robbed the party of one of its most effective spokesmen and debaters. Charles Black, a close friend of Atwater's and a veteran Republican political operative, filled in as spokesman during the 1990 campaign, but Bennett is expected to be a more powerful debater with the Democrats than was the soft-spoken Black.

Democratic National Committee Chairman Ronald H. Brown issued a statement last night welcoming Bennett to the fray.

"If Bennett accomplishes as much for the Republicans as he achieved at the Education Department and ridding us of drugs and violence, America will have to begin worrying about the future of the two-party system," Brown said. "I look forward to a vigorous debate over the solutions to our country's obvious economic problems."

The RNC slashed its staff by more than 25 percent last week. Party officials said the cuts were necessary to shrink the organization because there are few campaigns next year.