In a televised address Mr Clinton told the American people that he took full responsibility for his actions.
He said: "Indeed I did have a relationship with Ms Lewinsky that was not appropriate. In fact, it was wrong."
Aides close to the president now hope the confession will bring an end to the investigation into Mr Clinton's affairs, brought by independent prosecutor Kenneth Starr.
Mr Starr's four-year inquiry began as an investigation into land deals by Hillary and Bill Clinton when he was governor of Arkansas.
It moved onto his personal life when Mr Starr began to investigate allegations that Mr Clinton had had sexual relations with Monica Lewinsky and then lied about it under oath in a sexual harassment case brought by Paula Jones in 1994.
'I misled the people'
The president's confession follows months of denial. On 26 January this year, Mr Clinton categorically denied having sexual relations with Miss Lewinsky.
Appearing serious and contrite, Mr Clinton told the American people: "I misled people, including my wife. I deeply regret that.
He concluded: "This matter is between me, the two people I love most - my wife and my daughter - and our God."
He said he had not come clean earlier because he was embarrassed but he denied he had asked anyone to lie about the relationship.
He also criticised Mr Starr and the investigation, which so far has cost £25m.
On 6 August this year Ms Lewinsky told the jury that she had an 18-month sexual relationship with the President and that the pair had discussed ways of concealing the relationship.
She also presented one of her dresses as evidence, stating it had been stained with Mr Clinton's semen during one of their sexual encounters.
If it is proved that he lied he faces possible impeachment hearings on Capitol Hill.
Source: bbc
