A New York judge ruled Tuesday that Harvey Weinstein can be extradited to Los Angeles, paving the way for the former Hollywood producer to face sex-crimes charges in California after more than a year of delays because of the pandemic and his health.

Mr. Weinstein could be turned over to California authorities as soon as the middle of next month. He is currently serving a 23-year sentence at a maximum-security prison near Buffalo, N.Y., where his attorney said he was undergoing medical treatment.

Mr. Weinstein challenged the extradition, arguing that Los Angeles prosecutors hadn’t properly completed the paperwork seeking his transfer and that he wouldn’t receive adequate medical care in a West Coast jail.

“Prisons are designed for long-term incarceration. Jails are not,” said an attorney for Mr. Weinstein on Tuesday, arguing that his client should remain in the New York facility until jury selection begins in the California case.

Prosecutors in New York’s Erie County, where Mr. Weinstein’s prison is located, handled arguments for why Mr. Weinstein should be extradited to Los Angeles. They said Mr. Weinstein was certainly entitled to medical treatment but shouldn’t be able to dictate where.

“It’s not like this is some remote outpost without medical care,” said Colleen Gable, an Erie County assistant district attorney. “Los Angeles has some of the best medical care in not only this country, but the world.”

Erie County Court Judge Kenneth Case denied Mr. Weinstein’s request.

Mr. Weinstein has previously denied all allegations in New York and California, where he hasn’t been arraigned and so hasn’t entered a plea.

A spokesman for Mr. Weinstein on Tuesday said he would appeal the New York decision in hopes of preventing the extradition until he receives proper medical care.

A Manhattan jury in February 2020 convicted Mr. Weinstein of first-degree criminal sexual act, for forcing oral sex on “Project Runway” production assistant Miriam Haley in 2006, and of third-degree rape, for nonconsensual sex with then-aspiring actress Jessica Mann in 2013. He was acquitted of the most severe charges, which carried a possible life sentence—two counts of predatory sexual assault for the alleged rape of former “Sopranos” star Annabella Sciorra in the early 1990s.

In April, his attorneys appealed the conviction and requested a new trial.

Los Angeles prosecutors first announced sex-crimes charges against Mr. Weinstein on Jan. 6, 2020, the day that his criminal trial opened in New York. The Los Angeles prosecutors filed additional charges twice last year.

The allegations involve five accusers who alleged rape and sexual assault between 2004 and 2013.

Write to Deanna Paul at deanna.paul@wsj.com

Corrections & Amplifications
A Manhattan jury convicted Harvey Weinstein of first-degree criminal sexual act last year. An earlier version of this article incorrectly said the conviction was in February.