Tadashi Ishii said he would tender his resignation at a January board meeting.
Matsuri Takahashi, 24, jumped to her death in December last year and in a note left for her mother, she asked: "Why do things have to be so hard?".
She had started working at Dentsu in April 2015 and was soon doing an additional 100 hours a month.
Dentsu has been under pressure to reduce the amount of overtime its employees do and in November it was raided by labour regulators.
In September, the Japanese government ruled that Ms Takahashi's death had been caused by overwork. She would often return home at 5am after spending all day and night at the office.
Mr Ishii, who has been chief executive in 2011, said: "This is something that should never have been allowed to happen."
While Dentsu is attempting to curtail overwork - by turning off lights at the headquarters at 10pm - it admitted that more than 100 workers were still doing an extra 80 hours a month.
Death linked to exhaustion in Japan is so common that there is a word, "karoshi", to describe it. According to government figures, about 2,000 people a year kill themselves because of overwork.
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