President Reagan will nominate H. Robert Heller, director of economic research at the Bank of America, to become a member of the Federal Reserve Board, and Gov. Manuel H. Johnson to become the board's vice chairman, the White House announced yesterday.

Johnson, who joined the seven-member board in February, will succeed Preston Martin, who resigned at the end of last month as vice chairman. Heller will fill Martin's unexpired term on the board.

Both nominations require the approval of the Senate.

Heller, 46, has been senior vice president and director of economic research for the Bank of America since 1978. He is a former chief of financial studies for the International Monetary Fund and economics professor at the University of Hawaii.

The California economist is not widely known, but is well respected within the profession. C. Fred Bergsten, who heads the Institute for International Economics here, said of Heller, "He's primarily an international economist who's thought about the monetary system . . . He's a pretty pragmatic, balanced economist rather than a devout practitioner of any particular school."

Heller was graduated from Parsons College and holds a master's degree from the University of Minnesota and a Ph.D. from the University of California. He taught at the University of Hawaii from 1971 to 1974, and was chief of financial studies for the International Monetary Fund from 1974 to 1978.

Johnson, 37, who was assistant Treasury secretary for economic policy before being named to the Fed, formerly taught at George Mason University. He was graduated from Troy State University and holds masters and Ph.D. degrees from Florida State University.

Four members of the Fed board, Martin, Johnson, Martha Seger and Wayne D. Angell, joined in late February in a vote to reduce the Fed's discount rate over the objections of Fed Chairman Paul A. Volcker.

Before the vote was announced, however, Angell changed his mind, and the decision was held in abeyance until the central banks of West Germany and Japan agreed to reduce their rates, too.

In the aftermath of that vote, Martin pressed White House officials for a promise that he would be named to succeed Volcker as chairman when the latter's four-year chairmanship expires in August 1987. When no promise was forthcoming, Martin resigned to pursue private banking opportunities in California.

Last month, the discount rate was cut again, but that time Volcker joined the majority voting for the reduction. Johnson and Angell have indicated that they do not plan to be part of any clique on the board that would challenge Volcker's authority as its chairman.