Avenatti made the announcement on Twitter Wednesday morning, naming his client as Julie Swetnick. In the tweet, he described her as courageous, brave and honest.
The attorney also tweeted images of what he said was a sworn statement from his client, adding, "Under no circumstances should Brett Kavanaugh be confirmed absent a full and complete investigation."
Two other women have come forward with allegations of sexual misconduct against Kavanaugh.
MORE: 2nd woman claims sexual misconduct by Supreme Court nominee Brett Kavanaugh
Report: 2nd woman claims sexual misconduct by Kavanaugh
California professor Christine Blasey Ford has also accused Kavanaugh of sexually assaulting her at a high school party. Deborah Ramirez has also come forward with accusations against Kavanaugh. Ramirez said in a story published Sunday by The New Yorker Magazine that Kavanaugh placed his penis in front of her and caused her to involuntarily touch it during a drunken dormitory party.
Kavanaugh has staunchly denied that he ever sexually assaulted anyone. His allies, including President Donald Trump, have cast doubt on the accusations.
Ford and Kavanaugh are expected to testify separately at a committee hearing on Thursday.
The Associated Press contributed to this report.