Liu had been President Barack Obama's choice for the 9th U.S. Circuit Court of Appeals, but the nomination was blocked by Republicans. Liu eventually withdrew his candidacy.
Brown called Liu "an extraordinary man and a distinguished legal scholar."
The 40-year-old Georgia native graduated from Yale Law School. He clerked for U.S. Supreme Court Justice Ruth Bader Ginsberg and worked as an appellate litigator in Washington before joining the UC Berkeley faculty in 2003.
Liu would replace Justice Carlos Moreno, who announced his retirement earlier this year.
The Associated Press contributed to this report.