President Reagan yesterday announced the appointment of former representative Barber B. Conable Jr. as president of the World Bank and indicated he will look to him to remake the bank into the lead agency coping with the Third World's debt crisis.

The selection of Conable, 63, a highly respected moderate Republican, to succeed A. W. (Tom) Clausen ends a long struggle within the administration to find a president for the bank acceptable both here and abroad. The bank, which has 149 member governments, is the principal source of development loans for Third World borrowers.

Since he retired from Congress in 1984, Conable, who represented a district in western New York, has been a professor of political science at the University of Rochester in New York.

By tradition, the president of the World Bank has been an American, and the managing director of the International Monetary Fund a European, since the sister organizations were set up in 1944 at the Bretton Woods conference.

Hugh Foster, alternate executive director of the bank for the United States, formally presented Conable's name yesterday to a meeting of the bank's executive board. Technically, it is merely a nomination, but the United States, as the largest shareholder, effectively makes the appointment. Board ratification will be a mere formality.

Although the Reagan administration had been critical of Clausen's management of the bank and did not offer to reappoint him, yesterday's announcement made a point of praising his more recent performance. Clausen, Reagan said, "will leave behind an institution with a more effective set of tools to cope with the challenges to development in the coming years."

Conable's appointment comes at a critical time for the bank, which has been challenged by Treasury Secretary James A. Baker III to take a new and more decisive role in managing the Third World debt crisis, but which observers feared was drifting in the absence of an announcement of a new leader.

Attempts to reach Conable for comment yesterday were unsuccessful.

Congressmen of both parties and bankers in New York hailed the selection -- although development banking is not a main area of his background -- because of his experience on Capitol Hill.

Despite the Reagan administration's increasing commitment to providing funds for the World Bank and other multilateral development banks, Congress has made it clear that with the pressure of the Gramm-Rudman-Hollings law, it may not appropriate as much as the administration feels is necessary.

Administration sources expect that Conable, who served in Congress for 20 years and was highly regarded on both sides of the aisle, may be better able than anyone else to deflect some of the congressional antipathy to appropriations that are lumped under a "foreign aid" label, even if that is not precise.

Even though Clausen revealed in October that he would step down at the end of June, when his five-year term expires, squabbling within the administration had kept him in a lame-duck role with no prospect of a successor.

Baker, who had a major responsibility in the selection process, has been under increasing pressure to find someone for the post prior to the semi-annual steering committee meetings here of the bank and IMF on April 9 through 11.

The job had been turned down by Labor Secretary William E. Brock, and Conable's name arose only in the past two weeks after Europeans had objected strenuously to former Navy secretary J. William Middendorf as too conservative.

Middendorf, identified with right-of-center causes such as restoration of the gold standard, had little support either from Treasury or the State Department, which had put forward its own list of candidates. But he campaigned actively for the job, and many Europeans feared he would get it by default.

But when Brock -- who was heavily pressured by Secretary of State George P. Shultz to take on the assignment -- said no, Shultz and Baker agreed on Conable.

Conable reportedly also had the backing of Vice President George Bush, a close political associate, whom he has served as an informal adviser.

One source who identifies himself with the conservative wing of the Republican Party responded glumly to the news, saying, "we will have more of the same -- it's the status quo," meaning that Conable was not an improvement over Clausen.

A quick survey of a few European bankers indicated that they had little knowledge of Conable, and were surprised by the choice. But one added that "it's better than Middendorf or former Treasury secretary William E. Simon." Simon had indicated a willingess to take the job.

"It's a brilliant choice," said Norman Ornstein of the American Enterprise Institute. "It's the kind of appointment that will earn the administration a lot of political credits. Conable has the most penetrating mind of anyone I've ever seen on Capitol Hill."

Robert Hormats, a vice president of Goldman, Sachs & Co., and a former deputy assistant secretary of State, said, "He'll not only have great credibility on the Hill, but as a politician, he will have a lot of influence with the political leaders in the Third World."

Sir Roy Denman, head of the European Common Market delegation in Washington, said, "It is gratifying that a man with such keen awareness of international issues should be appointed to this very important post at such a critical time."