Michael Palmer, 44, a married father of one who was only sworn in as Speaker in October 2011, also quit his seat in parliament and membership of the ruling People`s Action Party (PAP).
"I have resigned to take full responsibility for a grave mistake that I have committed," Palmer told a press conference.
"My conduct was improper and it was a serious error of judgment. I have resigned in order to avoid further embarrassment to the PAP and to Parliament," he added.
Revealing that he "had a relationship" with a staff member of a community organisation called the People`s Association, Palmer, who is a lawyer, said he was "deeply sorry" to his supporters, the PAP as well as his family.
The association`s chairman is Prime Minister Lee Hsien Loong, who is also secretary-general of the PAP.
Lee quickly announced he had accepted Palmer`s resignation, saying members of parliament have to uphold the highest standards of conduct.
Deputy Prime Minister Teo Chee Hean, who was with Palmer at the press conference, apologised to residents of the disgraced politician`s constituency.
"I assure you that we will put things right and continue to look after you." There was no immediate word on a by-election to replace Palmer. Under Singapore law, a by-election is totally at the discretion of the prime minister.
The PAP, which has long cultivated an image of moral superiority over the opposition, came under immediate attack from online critics.
"The PAP needs to come clean with the people (about) what information have they got about Mr Palmer and in particular, what did they know about him prior to the May 2011 election," Adrian Lim, a member of the public, wrote on the prime minister`s Facebook page.
Palmer`s resignation is the latest high-level scandal to hit Singapore, which consistently ranks high in international surveys on government efficiency and cleanliness.
The former head of the narcotics police is on trial for allegedly seeking sexual favours from a contractor. The former head of civil defence is scheduled to be tried in January on a similar charge.
"Yes, certainly this is a blow to the PAP," said Reuben Wong, an associate professor in political science at the National University of Singapore.
He cited the PAP`s "relentless hectoring" of the opposition Workers` Party when one of its MPs, Yaw Shin Leong, was forced to quit politics over an extramarital affair earlier this year.
The Workers` Party, which regained the seat in a by-election, said Wednesday that it was ready to field a candidate against the PAP in Palmer`s former seat.
In another high-level sex scandal this year, 51 men including civil servants, businessmen and uniformed officers were charged in court for allegedly engaging the services of a 17-year-old prostitute, and some have been jailed.(*)