Archibald Cox, former Watergate special prosecutor and solicitor general of the United States, will be elected chairman of Common Cause at its national board meeting here today.

Cox, 67, will take over from Nan Waterman who has held the job three years. His term will be two years.

Common Cause, which says it has 229,000 members, was created 10 years ago as a self-described "citizens' lobby" to work for reform of corrupt political spending, an "unbought political system" and less political influence from special interests. It has been the chief proponent of public financing of federal election campaigns.

Cox, a Harvard law professor and author of several books, became famous in 1973 when he was appointed Watergate special prosecutor to look into the charges stemming from the Watergate break-in.

On the evening of Saturday, Oct. 20, 1973, President Nixon fired Cox for refusing to be satisfied with summaries of White House tape recordings and insisting that the full tapes be made available to his office.

Cox had already had a long public career before that. He was associate solicitor of the Department of Labor from 1943 to 1945 and was appointed U.S. solicitor general under President Kennedy in 1961, holding the office until 1965.

Cox is expected to retain his position at Harvard Law School while devoting about a third of his time to Common Cause business. The chairman is paid for the days he is on Common Cause business.