The actress, who was recently granted a leave of absence from hit medical drama Grey's Anatomy, started the adoption process more than six months ago with husband Josh Kelley, according to RadarOnline.com.
According to insiders, the adoption of 10-month-old Nayleigh will be complete by the end of the week (13Sep09), and the couple can take the baby home.
A source says, "She is thrilled. She and Josh are so happy."
Heigl recently hosted a star-studded baby shower party for pregnant Grey's Anatomy castmate Ellen Pompeo at her home.
She recently quit smoking in anticipation of becoming a mum.