President Reagan announced yesterday that he will nominate William J. Bennett, director of the National Humanities Center in North Carolina, to be chairman of the National Endowment for the Humanities.

The White House announcement comes after weeks of controversy and speculation. The other frequently mentioned candidate for the post, University of Dallas professor Melvin Bradford, waged a visible campaign that won him advocates as well as detractors.

Bennett, 38, has been president and director of the National Humanities Center in Research Triangle Park, N.C., since 1979. He is a registered Democrat who says he supports Reagan "enthusiastically." A graduate of Williams College in Massachusetts, Bennett holds a doctorate in philosophy from the University of Texas and a law degree from Harvard University.

He is the co-author, with Terry Eastland, of "Counting by Race: Equality From the Founding Fathers to Bakke," a 1979 book which is "critical of certain aspects of affirmative action," according to Bennett.

"The humanities form a vital part of our national heritage," said Bennett in a statement released yesterday, "and I would hope to improve appreciation and understanding of their importance in American culture."

Reached by phone yesterday, Bennett revealed no plans for his term at the NEH, a federal agency that makes grants to cultural and scholarly institutions as well as to individual scholars. "Well, first I'd like to be confirmed," he said. "As far as details and general policy go, I think I'll wait until I do my homework." He said he expects to be in Washington today to pay courtesy calls on senators.

Melvin Bradford, a staunch conservative and an academic who has written critically about Abraham Lincoln, reacted diplomatically yesterday to the news that Bennett would be Reagan's choice. "It was an honor to be considered," said Bradford in a phone conversation. "I congratulate Dr. Bennett on his nomination . In this, as in all other matters, I support the president completely."

Bradford's most fervent backer, Sen. John East (R-N.C.), was disappointed, if also conciliatory. "My own preference was for Dr. Bradford, who is well-qualified for the post," said East in a statement released by his office yesterday. "However, the president has selected Dr. Bennett, who is an able man, and I intend to support his nomination."