Tuesday, August 18, 1998 Published at 05:38 GMT 06:38 UK
President Clinton admits he "failed to volunteer information"
But in a defiant television address, the president said it was now a private family matter and "nobody's business but ours".
Earlier, lawyers led by the independent investigator, Kenneth Starr, questioned President Clinton for five-and-a-half hours in the White House, while a grand jury watched through a video link.
Relationship was 'wrong'
In his four-minute television address, the president said: "I did have a relationship with Miss Lewinsky that was not appropriate. In fact it was wrong.
It was the first time that President Clinton had admitted a sexual relationship with Miss Lewinsky.
During the previous seven months he had made denials on television and under oath in the Paula Jones sexual harassment case.
But the president insisted previous submissions had been legally correct and at no time had he asked anyone to lie or hide or destroy evidence.
"I misled people, including even my wife. I deeply regret that," he said.
"I can only tell you I was motivated by many factors. First by a desire to protect myself from the embarrassment of my own conduct. I was also very concerned about protecting my own family."
"This has gone on too long, cost too much and caused too much hurt to many innocent people.
"Now, this matter is between me, the two people I love most - my wife and our daughter - and our God.
"I must put it right, and I am prepared to do whatever it takes to do so.
"Nothing is more important to me personally. But it is private, and I intend to reclaim my family life for my family.
"It is nobody's business but ours - even presidents have private lives."
Mr Clinton ended his address by appealing to the American public to turn away from the spectacle of the past seven months.
"Our country has been distracted by this matter for too long and I take my responsibility for my part in all of this. That is all I can do. Now it is time - in fact it is past time - to move on.
"We have important work to do. Real opportunities to seize, real problems to solve, real security matters to face."
The president's lawyer, David Kendall, made a brief statement when the testimony to the grand jury ended.
The Clintons are due to travel to Martha's Vineyard for a two-week holiday on Tuesday.