According to People Magazine. "Katherine and Josh are adopting a baby," the actress's rep confirms to PEOPLE. The couple are adopting a girl from Korea; Heigl's sister also was adopted from Korea."
In another People article, Heigl is quoted as saying:
"She was actually born the day before me in November, which I thought
was really serendipitous and just kind of like a sign. I realized just
recently that I basically forfeited my birthday for the rest of my
As others have noted, it appears the couple received special considerations, since they have not been married long enough (3 years) to adopt according to Korean regulations. Especially since she reportedly began the adoption inquiry a year ago after being married only one year. Heigl says the adoption was expedited because the baby has special needs.
Here is Heigl talking about the adoption on Ellen vis Disgrasian.