RadarOnline.com reports that the couple's adoption process has been in the works for at least six months and that the 10-month-old girl is from Korea. The report also says the baby's name is Nayleigh, and her nickname will be Leigh.
Heigl plays Dr. Izzie Stevens on ABC's "Grey's Anatomy." Kelley is a singer-songwriter.
The couple have been married since 2007.