Premier Michel Rocard resigned Wednesday after three years in office and was replaced by Edith Cresson, a former Cabinet minister who becomes the first woman to head the French government.

The move was seen as a mutually desired divorce between Rocard and Socialist President Francois Mitterrand.Rocard, perennially popular with the public, is now free to pursue a possible presidential campaign in 1995 while Mitterrand can encourage Cresson to try new solutions to combat rising unemployment and other nagging problems.

A veteran of three previous Cabinet posts, the 57-year-old Cresson is best known for her combative appeals for an aggressive French response to economic challenges from Japan and Germany.

The announcement of the change in premiers, widely rumored for more than 24 hours, was made by Mitterrand's spokesman, Hubert Vedrine. Cresson was expected to announce a new Cabinet on Thursday, probably retaining many incumbent ministers.

Vedrine did not say why Rocard left office. There was no immediate statement from the 60-year-old Rocard, who had policy differences with Mitterrand but was not entangled in any specific controversies.

Cresson had been minister of European affairs until October, when she resigned and took a position with Groupe Schneider, a French industrial firm. She previously served as minister of agriculture, of foreign trade, and of tourism and industry.