Higgins said she felt she had to make a choice between reporting her allegations to police or continuing her career. She quit her government job in January last year and reported her allegation to police.
Higgins was one of seven women who were given exemptions from a pandemic ban on viewers sitting in the public gallery of the House.
Australian Prime Minister Scott Morrison thanked Higgins for the courage she had shown in making her allegations.
"I am sorry. We are sorry. I'm sorry to Ms Higgins for the terrible things that took place here," Morrison told Parliament.
"The place that should have been a place of safety and contribution turned out to be a nightmare. But I'm sorry for far more than that. For all of those who came before Ms Higgins and endured the same, but she had the courage to speak, and so here we are," Morrison added.
The Associated Press does not usually identify alleged victims of sexual assault, but Higgins has chosen to identify herself in the media.
More than 1,700 people made contributions to Jenkins' report, including past and present staffers.
Her report found 37 per cent of people currently in parliamentary workplaces had experienced bullying and 33 per cent had experienced sexual harassment.
Australian Deputy Prime Minister Barnaby Joyce told Parliament he joined in the apology and in "acknowledging that we will do better".
Revelations in 2018 that Joyce was expecting a baby with former press secretary Vikki Campion led to then-Prime Minister Malcolm Turnbull banning his ministers from having sex with staff. Morrison has maintained the ban.
Joyce in 2018 was married with four children. He has since married Campion with whom he has had two children.
House Speaker Andrew Wallace told Parliament action was already being taken to improve the workplace culture.
Last year, an independent complaints process was established. Lawmakers and staff had also undergone professional workplace training, Wallace said.
Higgins' former colleague Bruce Lehrmann has pleaded not guilty to a charge of sexual intercourse without consent and is scheduled to stand trial in a Canberra court in June.