11/16/2011 AT 07:00 AM EST
For years, Connie Britton has been hard at work on her acclaimed show Friday Night Lights
and most recently on the new hit American Horror Story
But the actress, 44, has just been cast in her most rewarding role yet: Mom. She's adopted a 9-month-old baby boy from Ethiopia, Britton tells PEOPLE exclusively.
After a three-year-long adoption process, the actress's dream of motherhood came true about a week ago, after she returned from the African country with her son Yoby – a nickname for Eyob, his given name.
"I am thanking my lucky stars every day," Britton, 44, tells PEOPLE.
The day she first held her son in her arms was something the new mom will never forget.
"It was such a wonderful moment of completion," she says. "I thought I was going to collapse into a puddle of tears. I was just grinning from ear to ear."