Mr Kan has been criticised for failing to show leadership after the devastating 11 March earthquake and tsunami, and ensuing nuclear crisis.
In June, Mr Kan pledged to quit if parliament passed three key pieces of legislation, which it did on Friday.
The ruling Democratic Party of Japan will choose a new leader on Monday.
Mr Kan's successor as party head will almost certainly become Japan's next prime minister.
Reports in Japan say Ichiro Ozawa, who leads the biggest faction despite the suspension of his party membership over a political funding scandal, is unlikely to support the former foreign minister.
Other possible successors include Finance Minister Yoshihiko Noda, Trade Minister Banri Kaieda, and Agriculture Minister Michihiko Kano.