The ruling Liberal Democratic Party will hold an internal election to pick a successor, likely to be Taro Aso, the party secretary general and ex-foreign minister, who must then be approved by the lower house of parliament.
"There cannot be a political vacuum from political wrangling.... We need a new team to carry out our policies," the outgoing premier said in a televised address.
He said "numerous long-running political and economic problems" had forced him to resign.
Fukuda's relatively brief premiership had been plagued by an economic slowdown and political divisions, with his party controlling the lower house of parliament, and opposition factions dominating the upper house.
Fukuda, 72, is the second Japanese premier to resign since Junichiro Koizumi left office two years ago. Shinzo Abe suddenly stepped down as premier in September 2007, also serving only one year in office.
