In public, Sandra Bullock has been through the best and worst of times this year – from winning her first Oscar to enduring the breakup of her marriage. In private, she was quietly keeping a joyful secret – his name is Louis, and he is her newborn son.

"He's just perfect, I can't even describe him any other way," Bullock reveals exclusively in the new issue of PEOPLE, announcing that she is the proud mother of Louis Bardo Bullock, a 3½-month-old boy, born in New Orleans. "It's like he's always been a part of our lives."

Bullock, 45, and husband Jesse James, 41, began the adoption process four years ago and brought Louis home in January but decided to keep the news to themselves until after the Oscars. Their close friends and family – including James's children Sunny, 6, Jesse Jr., 12, and Chandler, 15 – were essential in keeping the adoption a secret.

Then, just 10 days after the March 7 Oscars, Bullock and James separated following reports James had cheated. Bullock says she is now finalizing the adoption as a single parent.

For much more, including an in-depth interview with Sandra Bullock and exclusive photos of the star and her baby boy, pick up the new issue of PEOPLE, which hits newsstands Friday.