Donald P. Bogard, the controversial president of the Legal Services Corp., has submitted his resignation, effective Jan. 31, according to an agency spokesman.

Joel Thimell, an LSC spokesman, said that Bogard sent a letter of resignation, dated Dec. 31, 1984, to William C. Durant III of Grosse Point, Mich., the new chairman of the corporation's board of directors. Durant, who could not be reached for comment, notified other board members of Bogard's resignation over the weekend.

An agency spokesman told the Associated Press that Bogard "will continue as an adviser to aid in the transition."

There had been much speculation recently that the agency's new board of directors would ask Bogard to leave his $69,000-a-year job. President Reagan gave the 11 board members recess appointments late last year after they had failed to win Senate confirmation before the last Congress adjourned.

Bogard was appointed in October 1982 by another board of recess appointees whom the Senate had refused to confirm.

Many members of the poverty-law community were critical of Bogard's appointment because they believed that he and many members of the Reagan-appointed board wanted to dismantle the corporation.

Reagan, long a harsh critic of the program, tried several times to persuade Congress to reduce or eliminate the corporation's funding, but was not successful.

Bogard, 43, went to the corporation after spending much of his career in the Indiana attorney general's office and later serving as head of litigation for Stokely-Van Camp Inc., defending the company in suits brought by Legal Services Corp. lawyers on behalf of migrant farm workers.

To protect the LSC's programs, Congress placed several restrictions on the authority of Bogard and the agency's board, including severe limitations on their ability to cut grants to legal aid programs.

Despite administration efforts to cut back the program, the LSC's annual budget was increased by Congress from $241 million when Reagan took office to $305 million for fiscal 1985.

Thimell said Bogard's letter to Durant gave no reason for his resignation and that Bogard gave no indication whether he is leaving to accept a new job.

He said that the corporation's 140-member staff did not learn of Bogard's resignation plans until yesterday and that he knows of no candidates yet to fill the position.