U.S. marshals are accompanying Alcala on the trip. He will be arraigned in the strangling death of a flight attendant and a former Hollywood nightclub owner's daughter, whose body was found in 1978 after she disappeared the year before.
Two years ago, the former amateur photographer and dating-show contestant was convicted of killing a 12-year-old girl and four women in Southern California in the late 1970s.
Even if he's found guilty of the new charges in New York, he will likely be returned to California's death row. New York does not have a death penalty.
Alcala, now 68, is appealing his California convictions.
The Associated Press contributed to this report.