"I meet Ms. [name redacted] in Las Vegas," Cosby said in the deposition. "She meets me back stage. I give her Quaaludes. We then have sex. "
The woman was 19 at the time and a masseuse at a health club in Las Vegas, according to the documents obtained by PEOPLE.
Cosby said he had seven prescriptions for Quaaludes in the 1970s, according to portions of his deposition in the 2005 lawsuit filed by former Temple University employee Andrea Constand.
He kept those Quaaludes into the '80s, '90s and year 2000, his attorney, Patrick O'Connor, said in the court documents.
On Monday, a federal judge unsealed a motion from the 2005 lawsuit that included excerpts from Cosby's deposition at the request of the Associated Press. Several other documents were unsealed as well but not the deposition itself.
Joe Cammarata, who represents attorney Tamara Green and two other women who say Cosby drugged and sexually assaulted them in a defamation lawsuit against the actor, said the statements "support the victims' allegations against him."
"It's an extraordinary turn of events which provides much-needed public light on Mr. Cosby's behavior," he tells PEOPLE.
RELATED VIDEO: Bill Cosby Admits to Drugging Women to Have Sex with Them
Cosby's attorney did not immediately respond to PEOPLE's request for comment.
In 2005, Constand filed a civil suit against Cosby, alleging her drugged and groped her at his Elkins Park, Pennsylvania, mansion. Thirteen women – identified only as Jane Does – then came forward saying he'd done the same thing to them.
Cosby settled the lawsuit in November 2006 and his deposition was sealed. Last October, the allegations resurfaced after comedian Hannibal Buress called Cosby a rapist during a performance in Philadelphia. A cell phone video of the comments was posted online and quickly swept the Internet, prompting dozens more women to come forward with similar tales.
"We have been telling the truth," former model Beth Ferrier, who was Jane Doe Number 5 in Constand's lawsuit, tells PEOPLE. "Other Jane Does – come forward. It's safe now."
Cosby also testified he called someone from the William Morris Agency and "asked him to send money" to one of the witnesses in Constand's lawsuit, the documents say.
Cosby also said he "doesn’t remember" if he drugged Ferrier before having sex with her but "agreed to give an exclusive interview to the National Enquirer in March 2005 in exchange for their agreement to not print the Beth Ferrier story," the documents say.