Donald E. Graham has been named publisher of The Washington Post, effective today.

His appointment was announced by Katharine Graham, the board chairman and chief executive officer of The Washington Post Co., which includes Newsweek magazine, broadcasting stations and three newspapers, including The Post.

She is relinquishing to her son the title of publisher of The Post which she has held for 10 years, but she will continue her other corporate responsibilities.

Donald Graham, 33, has held a variety of positions with The Post Co. since 1971. In 1976 he was appointed executive vice president and general manager of The Post, succeeding Mark Meagher, who is now president of the company.

Graham was graduated from Harvard College, where he was president of The Harvard Crimson, the student newspaper. He served in Vietnam as a soldier with the First Air Cavalry Division and as a patrolman in the Washington, D.C., Police Department.

He joined the Post in 1971, and for four years worked in many departments of the newspaper -- as a reporter, assistant city editor, advertising salesman, circulator, market researcher, budget analyst and night production manager.

He then did a stint as a Newsweek writer in the New York and Los Angeles bureaus and returned to The Post as assistant managing editor in charge of the sports department.

He was appointed assistant general manager in 1975. In 1976 he succeeded Meagher and now succeeds his mother as publisher of the newspaper.

The Washington Post observed its 100th anniversary in December 1977. For nearly half of its existence it has been a family enterprise. Mrs. Graham's father, Eugene Meyer, bought the newspaper on June 1, 1933. He assumed the title of publisher, and retained it until 1946, when he was succeeded by his son-in-law, Philip L. Graham, the husband of Katharine and the father of Donald Graham.

Mrs. Graham became The Post's publisher in 1969. Donald Graham now becomes the fourth member of the family to fill that role.

Since 1971 The Post has been a publicly owned company, but control of the enterprise remains in the hands of the Graham family.

Since the paper's acquisition by Meyer more than 45 years ago, it has grown into a major communications corporation, which Mrs. Graham will continue to manage. In addition to its ownership of Newsweek, broadcasting stations and newspapers in Trenton, N.J., and Everett, Wash., the Washington Post Co. is a partner in the Los Angeles Times-Washington Post News Service, the International Herald-Tribune, Bowaters-Mersey Paper Co. Ltd., the Robinson Terminal Warehouse in Alexandria and a new newsprint manufacturing consortium in Southern Virginia.

Mrs. Graham is a director of the Associated Press, director and treasurer of the American Newspaper Publishers Association, board member of Allied Chemical Corp., a member of the Industrial Conference Board, a trustee of George Washington Univesity and the University of Chicago and is actively involved with the Independent Commission on International Development Issues, popularly known as the Brandt Commission.

Donald Graham is married to the former Mary Whistler, a lawyer. They have two children and live in the Cleveland Park area of Washington.

The directors of The Post Co. meet today to formally ratify his selection as publisher of the newspaper.

The Post in 1978 reported the highest circulation, advertising lineage and earnings in its 101-year history.