Weinstein was convicted in New York in February 2020 for sexual assault and rape and was sentenced to 23 years in prison.
In Los Angeles, he is wanted for trial on charges of attacking five women from 2004 to 2013.
The Los Angeles charges include forcible rape, forcible oral copulation, sexual battery by restraint, and sexual penetration by use of force. If convicted, Weinstein could spend the rest of his life in prison.
"This morning at approximately 9:25 custody of Mr. Harvey Weinstein was handed over to the appropriate officials for transport to the state of California per a court order," the New York Department of Corrections said in a statement.
Weinstein, 69, is appealing his New York conviction and sentence, and has denied having nonconsensual sex with anyone.
He has been fighting extradition to California on medical grounds, citing diabetes and cardiac, back and eyesight problems.
"We will be fighting so that Harvey can receive his needed medical care and of course, so that he can be treated fairly. Due process, presumption of innocence and a fair trial are all still his right," his spokesman Juda Engelmayer said in a statement on Tuesday.The Los Angeles District Attorney's office said on Tuesday it had no information to share at this time.
Weinstein was one of the most powerful movie and TV producers in Hollywood before allegations by more than 80 women of sexual misconduct in 2017 led to criminal charges and fueled the wider #MeToo movement.
He co-founded the Miramax film studio, whose hit movies included "Shakespeare in Love" and "Pulp Fiction." His own eponymous film studio filed for bankruptcy in March 2018.