The facility in Harrison will be sold to St. Joseph's Medical Center in Yonkers.
A hospital spokeswoman says the transaction must be approved by bankruptcy court. The transfer will then have to be approved by the state Department of Health and other state agencies.
The Westchester facility provides mental-health and substance-abuse treatment for children, and adults.
The city's last Catholic-affiliated hospital filed for bankruptcy before closing in April, citing a debt topping $1 billion dollars.