Bullock, 45, has been keeping a low profile since allegations became public last month that James, her husband of five years, cheated on her with several different women. The claims were made shortly after Bullock won her first Oscar for her work in "The Blind Side."
The actress told People she and James started the adoption process four years ago and brought now 3 1/2-month-old Louis home to California from New Orleans in January.
Bullock told the magazine she and James decided to keep the baby news quiet until after the Oscars, but then weren't able to announce it as planned because of the salacious stories emerging about their marriage. She now describes herself as a single parent, an excerpt from the magazine's interview said on its Web site.
Although the Web site doesn't feature quotes from the actress regarding the meltdown of her marriage, it does show a photo of the magazine's cover depicting Bullock gazing lovingly at her new son. A pull quote on the cover attributed to her says, "I have filed for divorce."
"He's just perfect, I can't even describe him any other way," Bullock said of little Louis in the excerpt on People.com. "It's like he's always been a part of our lives."