"I don't know how we got away with it," Bullock told People magazine in an exclusive interview that will be on newsstands Friday.
Bullock, 45, said friends and family, including her stepchildren -- Sunny, 6, Jesse Jr., 12, and Chandler, 15 -- were instrumental in helping the actress keep her newly-adopted son, Louis Bardo Bullock, a secret.
She also revealed to the magazine that she had filed for divorce from James, 41, and will raise "Louie" as a single mother.
Bullock filed legal papers in Travis County Court in Austin, Texas, April 23. Bullock claimed "the marriage between Petitioner and Respondent has become insupportable because of discord or conflict of personalities that destroys the legitimate ends of the marriage relationship and prevents any reasonable expectations of reconciliation," according to the documents.
She also said in the documents that "there is no child under eighteen years of age or otherwise entitled to support who was born or adopted of this marriage and none is expected," despite Louis' having been placed with Bullock and James before their marriage collapsed.
In the People article, Bullock expressed surprise that no one had caught on to her secret. On Oscar night she said one of Louis' lime green socks kept falling out of her purse and people would pick it up and hand it to her without saying anything.
In hindsight, she may have dropped a hint about her new bundle of joy during her acceptance speech for best actress for her role in "The Blind Side."
"I would like to thank what this movie was about for me, which are the moms that take care of the babies and the children no matter where they come from," she said.
The parallels between the character Bullock played in "The Blind Side," real-life Memphis mom Leigh Anne Tuohy and what was happening in her real life were not lost on the actress.
"I had to smile at the parallels," she told People. "Here I was promoting a story about a family who adopted a son, and here we were having done the same thing."
Like Tuohy's adopted son, NFL star Michael Oher, Louis is black.
Quinton Aaron, the actor who played Bullock's son in the movie, has no doubt she'll make a great mom.
"I am truly overjoyed for Sandra -- what amazing news and so special that she has been able to keep this time private between her and the baby!" he told People magazine. "Just as she played an exceptional mother in The Blind Side, her caring nature will make her an amazing mother to Louis!"
Though Bullock and James began the process of adopting four years ago, they did not get a call that there was a possible placement until January, in the middle of awards season. Bullock said she kept Louis a secret then because she didn't want him pulled into the middle of the craziness.
Sandra Bullock Gets By with Friends, Family
"We only told a handful of family and friends, and it then became their mission to make sure Louis was safe and happy and had everything he needed," Bullock told the magazine.
"Her inner circle is very tight," Popeater columnist Rob Shuter told ABCNews.com. "I hear that very, very few of her friends knew."
Doctors' visits became like CIA missions, Bullock said, with decoys and dark cars. And the couple managed to arrange a bris, a Jewish circumcision ceremony, because they couldn't have the procedure done in a hospital without tipping off the media.
"I don't think we would have had that special an experience had our situation been anything other than the secret world of Louis that we lived in," Bullock said. "It allowed us to spend every waking moment with our little man."
It also meant fittings for Oscar dresses had to be done outside the home and that Bullock got little sleep while taking care of Louis without hired help.
"She really, really relies on close relatives and friends and she doesn't hire help -- they're the people who normally gossip," Shuter said.
Bullock has relied on them even more since her split last month from James after she learned of his alleged infidelities.
"She has been hiding with the baby since the scandal broke," People magazine senior editor David Caplan said. "She said that when she found out about Jesse's affairs, she grabbed Louis, she grabbed their stuff, and she left."
Bullock said, "All I remember is thinking, 'I need to get Louis out of here before the vultures descend.' I wasn't sure if I could go into deeper hiding than I had already been in, but again, that small group of friends and family made it their life to make sure we all had what we needed to heal and be safe and make sense out of all of it."
Still to be worked out are what role James will play in Louis' life.
James, who recently completed 30 days in rehab, told People, "The decision to let my wife end our marriage and continue the adoption of Louis on her own has been the hardest. The love I have for Louis cannot be put into words. Not having him around to love and to hold has left a huge hole in my heart."
Bullock, for her part, said, "I really don't know how our paths will intersect in the future, but the father I have known Jesse to be with all the kids is one that I hope Louis can experience one day, no matter how Jesse and I go on with our lives."
She added that James' children, regardless of what their relationship to her is "on paper" will continue to be a part of her and their brother's life.
Now that her secret is out, Bullock said she's looking forward to being like other proud moms: "Telling everyone I meet about the most beautiful man I know, including his poop schedule."
ABC News' Sheila Marikar contributed to this report.