The 69-year-old had suffered from cardiac, dental and back problems but on 15 June Erie County Court Judge Kenneth Case dismissed his appeal, paving the way for Weinstein to be moved west.
“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.
More on Harvey Weinstein
The Los Angeles charges include forcible rape, forcible oral copulation, sexual battery by restraint, and sexual penetration by use of force.
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A New York judge has ruled Harvey Weinstein can be extradited to California to face rape and sexual assault charges.
If convicted, Weinstein could spend the rest of his life in prison.
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 fuelled the wider #MeToo movement.
He co-founded the Miramax film studio, whose hit movies included “Shakespeare in Love” and “Pulp Fiction.”