Pitt confirmed Paltrow's version of events to the Times but offered no further comment on the subject.
In the same interview, his estranged wife Angelina Jolie identified herself as another victim.
They join Asia Argento, Rose McGowan, Ashley Judd, Rosanna Arquette and Mira Sorvino who all say they were at some point sexually harassed by Weinstein over the last 30 years.
In her interview on Tuesday, Paltrow told how Weinstein was afraid she was going to lose the title role in Emma, Weinstein's 1996 adaptation of the Jane Austen novel, when the incident in his room occurred.
"I was a kid, I was signed up, I was petrified," Paltrow recalled.
She rebuffed him and left promptly, later telling Pitt about the encounter.
Paltrow, the daughter of Hollywood legends Blythe Danner and Bruce Paltrow who grew up mingling with the industry's biggest stars, said she recalled thinking: 'I thought you were my Uncle Harvey'.
After Pitt confronted Weinstein, the mogul phoned Paltrow and allegedly told her to never mention it to anyone else.
Paltrow, who has taken a backseat from acting in recent years to spearhead her lifestyle and wellness business Goop, said she feared her career would be over if she did not comply.
"I thought he was going to fire me. He screamed at me for a long time. It was brutal," she said.
They continued to work together and both enjoyed meteoric success as a result of the partnership with Paltrow winning an Oscar in 1999 for her role in Weinstein's Shakespeare In Love.
She resigned herself to never speaking of the incident, admitting: "I was expected to keep the secret."
The actress, 45, said she had decided to finally speak out against Weinstein - who she described as "alternately generous and supportive and championing, and punitive and bullying," to send a message.
"We're at a point in time when women need to send a clear message that this is over. This way of treating women ends now," she said.
She lamented the fact that her agents had set up the meeting and told how she trusted she would be in safe hands because they had set it up.
"It's on the fax, it's from C.A.A.," she said of seeing the appointment pencilled in to her schedule. Paltrow moved from C.A.A. to United Talent Agency in 2008.
Other actresses have told how Weinstein lured them to hotel rooms under the pretense of business meetings but said that staff and assistants disappeared once they were there.
Pitt and Paltrow dated from 1994 to 1997. He married Angelina Jolie, another of Weinstein's unsuspecting victims, in 2014.
In an email to the New York Times on Tuesday, Jolie, who has since separated from Pitt, admitted she was once also targeted by Weinstein in the same way.
"I had a bad experience with Harvey Weinstein in my youth, and as a result, chose never to work with him again and warn others when they did.
"This behavior towards women in any field, any country is unacceptable," Jolie said.
Their encounter was in 1998 during the release of her film Playing by Heart.
Jolie and Paltrow are the latest stars to break their silence on the scandal that has been engulfing Weinstein since The New York Times revealed last week that he was the subject of decades-old allegations of sexual harassment.
