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The agreement for Christine Blasey Ford to testify came just hours before the New Yorker magazine published an article in which a second woman, identified as Deborah Ramirez, described another instance of alleged sexual misconduct by Kavanaugh, also in the 1980s, when both attended Yale University.
Ford's agreement to testify before the Senate Judiciary Committee came a week after she went public in an interview in the Washington Post with her allegation that Kavanaugh sexually assaulted her in 1982 when both were high school students in Maryland.
Her allegation against the conservative federal appeals court judge has endangered his confirmation by the Republican-led Senate to a lifetime job on the top US court.
Kavanaugh has also agreed to testify at the Senate Judiciary Committee hearing planned for 10 a.m. (1400 GMT) on Thursday.
The potentially explosive hearing, set against a backdrop of the #MeToo movement fighting sexual harassment and assault, comes just weeks before Nov. 6 congressional elections in which Democrats are trying to take control of Congress from Trump's fellow Republicans.
The New Yorker magazine reported that Senate Democrats are investigating the new allegation against Kavanaugh that dates to the 1983-84 academic year, when Kavanaugh was a Yale freshman. Ramirez is cited by the New Yorker as saying Kavanaugh exposed himself to her during a drunken dormitory party.
Kavanaugh has called Ford's allegation "completely false" and said in a statement provided by the White House on Sunday night the incident described by Ramirez "did not happen."
"This is a smear, plain and simple," Kavanaugh said.
"I look forward to testifying on Thursday about the truth, and defending my good name - and the reputation for character and integrity I have spent a lifetime building - against these last-minute allegations," Kavanaugh said in the statement.
White House spokeswoman Kerri Kupec called the new allegation part of a "coordinated smear campaign by the Democrats designed to tear down a good man."
"The White House stands firmly behind Judge Kavanaugh," Kupec said.
The magazine said it has not confirmed with other eyewitnesses that Kavanaugh was present at the party at issue in Ramirez's account.
After the New Yorker article was published, Senator Dianne Feinstein, the Judiciary Committee's top Democrat, wrote to the panel's Republican chairman, Senator Chuck Grassley, asking for an "immediate postponement of any further proceedings" on Kavanaugh's nomination.
"I also ask that the newest allegations of sexual misconduct be referred to the FBI for investigation," Feinstein wrote.
Grassley's spokesman, Taylor Foy, accused Senate Democrats of withholding information on the latest allegation and of seeking a "political takedown" of Kavanaugh. He did not offer any evidence, except to cite the New Yorker report that the committee's Democratic staff were made aware of the allegations.
"Of course, we will attempt to evaluate these new claims," Foy said in a statement, adding that the committee's Republican staff only learned of Ramirez's allegation from the New Yorker article on Sunday evening. The New Yorker story, however, said senior Republican staffers were informed last week.
Ford, a psychology professor at Palo Alto University in California, has said Kavanaugh sexually assaulted her in 1982 when both were high school students in Maryland. She accused him of attacking her and trying to remove her clothing while he was drunk at a party when he was 17 years old and she was 15.
There are still unresolved procedural and logistical issues regarding Ford's testimony, her lawyers said, including whether the Judiciary Committee's Republican senators, who are all male, or staff attorneys would question her. Ford's lawyers said "various senators have been dismissive of her account and should have to shoulder their responsibility to ask her questions."
Ford's lawyers said that, in a Sunday morning call with committee staff members, they agreed to the hearing even though the committee refused to subpoena Mark Judge, a Kavanaugh friend who Ford said witnessed the attack, as well as others she said were present.
"Despite actual threats to her safety and her life, Dr. Ford believes it is important for senators to hear directly from her about the sexual assault committed against her," Ford's attorneys Debra Katz, Lisa Banks and Michael Bromwich said in a statement.
"She has agreed to move forward with a hearing even though the Committee has refused to subpoena Mark Judge," it said. "They have also refused to invite other witnesses who are essential for a fair hearing that arrives at the truth about the sexual assault."
Grassley had set several deadlines since Friday for Ford to decide whether and how she would testify before the panel.
"Following Dr. Ford's testimony, Judge Kavanaugh will appear again before the committee," according to a statement from the committee.
Kavanaugh was questioned by committee staff last week.
Grassley's counsel said in a note to Ford's lawyers that "the Chairman asked me to relay again that he will do everything in his power to provide a safe, comfortable and dignified forum for Dr. Ford to testify." The counsel said it was the committee's "non-negotiable" right to determine who would be allowed to testify.
Kavanaugh's confirmation would solidify conservative control of the Supreme Court and advance Trump's goal of moving the high court and the broader federal judiciary to the right.