The Oscar-winning actress is reported to have told the magazine that she adopted Louis Bardo Bullock in January but wanted to keep the news quiet until after the Oscars.
The 3-month-old baby was born in New Orleans.
"It's like he's always been a part of our lives," she is quoted as saying.
Bullock, 45, is thought to have told the magazine that she began the adoption process with estranged husband Jesse James, who was recently accused of cheating on her with women including tattoo model Michelle McGee. The actress said that she is now adopting as a single parent.
She is also reported to have confirmed she is starting divorce proceedings against James, admitting that she is "sad and scared".