Rao currently serves as Trump's top official on regulatory matters. Trump, whose administration has reversed a succession of regulations on the environment and other issues since he took office last year, made the announcement during a White House ceremony in honor of Diwali, a Hindu festival. Rao's parents are Indian.
"She's going to be fantastic - great person," Trump said.
"Thank you very much, Mr. President, for the confidence you've shown in me. I greatly appreciate it," Rao said.
If confirmed by the Senate, which is controlled by Trump's fellow Republicans, Rao would replace Kavanaugh on the U.S. Court of Appeals for the District of Columbia Circuit, which hears most major cases over the lawfulness of federal regulations.
Before joining the administration, she was a law professor at George Mason University in Virginia. She also served as a clerk for conservative Supreme Court Justice Clarence Thomas.
The Senate confirmed Kavanaugh on Oct. 6 after a contentious political fight in which the nominee denied allegations of sexual misconduct dating to the 1980s.
By replacing Kavanaugh, Rao would not change the ideological balance of the appeals court, which has a majority of Democratic-appointed judges.
(For a graphic showing Trump's impact on federal appeals courts, click tmsnrt.rs/2PPsGtM )
(Reporting by Lawrence Hurley; Editing by Will Dunham)
(This story has not been edited by Devdiscourse staff and is auto-generated from a syndicated feed.)