Baptist Hospital said, however, all non-local pregnant women will have to pay the same price. A spokeswoman for the hospital said mainland wives of Hong Kong residents might get extra beds or be put on a waiting list as all maternity beds for this year have been reserved.
The three other hospitals that have agreed to accept them are Union, Precious Blood and St Teresa's.
Union Hospital has promised to charge eligible mainland women at the price fixed for local mothers between HK$40,000 ($5,200) and HK$50,000. Non-locals giving birth at public hospitals are currently paying HK$39,000 if they have an advanced booking.
The city's 12 private hospitals had agreed the day before to refuse obstetric services to mainland women who are not married to local residents from next year.
Incoming Chief Executive Leung Chun-ying, who has vowed to impose a "zero quota" policy for non-local women giving birth at private hospitals from next year, welcomed the decision on Wednesday.
"There are legal issues for us to work on, but I think the decision will help us solve the problem," he said. "We're progressively heading in the right direction in solving the problem brought by mainland women giving birth in Hong Kong."
To secure beds this year, an eligible mother-to-be must present a marriage certificate and the original copy of her husband's identity card when making a reservation. The couple must also provide a notary certification and authorize the Hong Kong government to cross-check the documents if they were married on the mainland.
The husband must further sign an affidavit confirming the authenticity of their marriage. As forging a document and perjury are liable to imprisonment of 14 years and seven years, respectively, Chow said the deterrent is big enough. "I believe Hong Kong men will not be used in that way," he said.
Presentation of notary proof could be waived for mothers expecting before the end of May.
Chow said hospitals are not legally obliged to comply with the new rules, saying he saw no reason for hospitals to admit ineligible mothers. "Though we think the measure is generally workable, I cannot say it's totally leak-proof," he said.
Health officials will conduct random tests in future. Chow suggested if a mother due for delivery in July had only got married in May, she would look suspicious enough for further examination.
He also suggested public hospitals could spare beds for locals' mainland wives next year, but beds for this year have been fully booked.