Beryl Sprinkel's resignation as chairman of the Council of Economic Advisers was announced yesterday by the White House, and he said he plans to join a number of corporate boards while writing and speaking about economic issues and perhaps teaching.

Sprinkel, 63, submitted his resignation nine days ago to President Reagan, who accepted it yesterday. Sprinkel told Reagan he was leaving "with great reluctance ... for personal reasons."

In the letter, which was released by the White House, the CEA chairman called his service in the Reagan administration, first as undersecretary of Treasury for monetary affairs from 1981 to 1985 and at the Council since, a "treasured experience."

The president's letter accepting the resignation praised Sprinkel and cited a long list of his accomplishments. "As one of the original members of my team, you have served this administration selflessly for what will be almost seven years," Reagan said. "During that time, you have been one of the most articulate advocates of its philosophy and one of its most able officials."

Sprinkel said he and his wife, Barbara, will return to the Chicago area where he had been the chief economist at Harris Bank & Trust Co. before coming to Washington in 1981.

In an interview yesterday, Sprinkel declared, "I am not about to make any kind of commitment until I get out of here. That would not be appropriate.

"But I have thought I would take a limited number of board memberships. ... I will also do some public speaking, which I enjoy. I enjoy the public policy arena. I will also write some, but probably not a book. I've done that three times."

The CEA chairman said he will be 64 in November, adding, "I don't intend to go back to 10- and 12-hour days."

But he also stressed that he had no intention of going into a true retirement.

At the CEA, Sprinkel has kept a much lower public profile than his predecessor, Harvard economist Martin Feldstein, who angered the White House by publicly pushing for action to reduce the federal budget deficit even if it required a tax increase.

Feldstein actually was urging adoption of what was official administration policy, but it was a policy that neither the president nor his close aides wanted to see put into place.

After Feldstein resigned in 1984, the CEA chairmanship was left vacant for more than half a year and some White House officials wanted the council abolished.

Sprinkel said he talked with the president about the status of the CEA when he was offered the chairmanship in January 1985.

"The chairman had been gone six or eight months, and they were thinking of dropping the council. When Don Regan {who had just become White House chief of staff} asked whether I was interested, I said that I was if he and the president would put the council back into the policy process. If they would help me reorient it and make it useful again, I would take the job.

"They delivered, and I have worked very hard at restoring it," Sprinkel said.

During Reagan's second term, the CEA had become actively involved in the Domestic Policy Council at the White House and other policymaking groups and "I think it is performing very, very well," he continued. "I have access to the president."

He said he had urged Reagan to consider both Thomas Gale Moore and Micheal Mussa, the other two members of the council, for the chairmanship.