Her departure is the latest in a string of resignations among top executives at the company.
Edwards joined Yahoo in 1996 as employee number 19. She has been credited with creating and maintaining the company's strong brand identity, summed up by the famous advertising strapline "Do you Yahoo!?".
She leaves in early October for personal reasons and to spend more time with her two-year-old son.
Yahoo!, which is suffering like many dotcoms in the advertising downturn, has lost a number of executives who joined during the company's early days.
Heather Killen, head of international operations, and Anil Singh, head of sales, both resigned earlier this year. In February, Yahoo! Europe lost its managing director Fabiola Arrendondo and, a month later, Yahoo! Canada's managing director Mark Rubinstein resigned.
The company's CEO Tim Koogle stepped down in March, to be replaced by film industry veteran Terry Semel.