In Vanity Fair magazine, Monica Lewinsky, 40, writes that she deeply regrets the fling.
The president “took advantage” of her, she writes, though she describes their relationship as consensual.
In 1998, Republicans failed in their effort to oust him from office on the grounds he had lied about the affair.
But with Mr Clinton’s wife Hillary said to be mulling a 2016 run for the presidency, the Lewinsky matter has remerged in US political discourse, in part because Republicans are eager to wield it against her.
In an advance excerpt of the article released by Vanity Fair, Ms Lewinsky writes she hopes to reclaim her story and says she is still recognised every day and sees her name thrown about in pop culture and the news media.
“I, myself, deeply regret what happened between me and President Clinton,” she writes.
“Let me say it again: I. Myself. Deeply. Regret. What. Happened.”
Ms Lewinsky writes that she suffered abuse and humiliation after the scandal broke in 1998, in part because she was made a “scapegoat” to protect the president.
“The Clinton administration, the special prosecutor’s minions, the political operatives on both sides of the aisle, and the media were able to brand me,” she wrote.
“And that brand stuck, in part because it was imbued with power.”
Arguing Mr Clinton had lied to federal investigators about his relationship with Ms Lewinsky, who was in her early 20s, the Republicans in the House of Representatives impeached the president, essentially bringing him up on charges in the Senate to determine whether he could be expelled from office.
That effort failed, and Mr Clinton served in the White House until his term ended in 2000.
Hillary Clinton, meanwhile, went on to be elected US senator and to serve as secretary of state under President Barack Obama, and is currently tipped as a frontrunner for the Democratic 2016 presidential nomination.
The Republicans have indicated recently that Mr Clinton’s affair with Ms Lewinsky will be fair game should Mrs Clinton indeed run.
Republican Senator Rand Paul – also tipped to run for the presidency in 2016 – said this year that “bosses shouldn’t prey on young interns in their office”.
Mr Clinton “took advantage of a girl that was 20-years-old and an intern in his office”, he added. “There is no excuse for that and that is predatory behaviour.”
In her piece, Ms Lewinsky signals that her desire in breaking her silence after so many years is to “give a purpose” to her past.
“Perhaps by sharing my story, I reasoned, I might be able to help others in their darkest moments of humiliation,” she writes.
Ms Lewinsky now aims “to get involved with efforts on behalf of victims of online humiliation and harassment and to start speaking on this topic in public forums”.