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.
On Wednesday, 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.

The 35-year-old has been without a club since  at the end of last season.
Morrison scored nine goals in 36 games for Ireland and was part of their squad at the 2002 World Cup.
The striker is available to play for Exeter in their League Two game at Accrington on Friday night.
Morrison began his career at Palace in 1997 and scored 71 goals in 181 games before moving to Birmingham City for club-record fee of £4.25m in 2002.
After three seasons at St Andrews he returned to Palace for £2m before moving to Coventry City in 2008.
He spent two seasons at the Ricoh Arena before moving on to Sheffield Wednesday, and after loans at MK Dons and Brentford, joined Colchester in 2012.

Wanda Campbell, 43, of Auchenmalg near Newton Stewart, was jailed for three years earlier this month.
She was also ordered to pay compensation of £110,000 at Dumfries Sheriff Court.
Her appeal against that sentence and the conviction will be heard at the Appeal Court in Edinburgh.
She was found guilty after a seven-day trial of acting with others to take the money from James Haugh Castle Douglas between March 2012 and October 2013.
The head of Japanese advertising group Dentsu is to step down following the suicide of an employee who had worked hundreds of hours of overtime.
[NEXT_CONCEPT]
Exeter City have signed former Republic of Ireland, Crystal Palace and Birmingham City striker Clinton Morrison on non-contract terms.
[NEXT_CONCEPT]
A woman found guilty of conning a south of Scotland garage firm out of £110,000 has lodged an appeal against her sentence and conviction.