The ban will restrict any Hong Kong-born children of mainlanders from receiving residency.
Leung said the legislation will also apply to private hospitals, though mainland mothers with local resident husbands will be exempt.
The city has not yet decided on the quota for foreigners giving birth in public hospitals in 2013.
“We are now holding discussions with private hospitals, and at the same time continuing communication with the chief executive-elect,” the Food and Health Bureau said.
Leung’s announcement follows a 1,500-strong protest in January over growing numbers of Chinese births.
The city’s Census and Statistics Department said the number of Hong Kong-born infants in the decade to 2010 nearly doubled due to 232,536 mainland-Chinese births.