The baby boy, who was born just before 2 a.m. Tuesday at a Los Angeles hospital, was delivered via a scheduled C-section.
"Kevin had a smile on his face. He looked happy and upbeat," says an observer.
The whole thing, says a source, was smooth – just as the mom-to-be had predicted to PEOPLE back in August, saying childbirth "will be a piece of cake."
Spears, 24, and Federline, 28, already have a son, Sean Preston, who was born Sept. 14 last year. For Federline, the new arrival is his fourth child. He also has a daughter Kori, 4, and son Kaleb, 2, with actress Shar Jackson.
Spears first publicly confirmed this pregnancy during a May 9 visit to the Late Show with David Letterman. "Don't worry, Dave, it's not yours," she joked to the host, who responded: "Oh. Well, I think that's good news for both of us."
The timing of baby No. 2's arrival may have been a surprise – Spears has said the pregnancy wasn't planned – but expanding her brood was never a question for the domesticity-craving pop star. Sean Preston "is going to be traveling on the road with me, so I think it will be good to have (a sibling) there with him," she told PEOPLE last month.
For Federline's part, the aspiring rapper told PEOPLE after his performance at the Teen Choice Awards last month, that he planned to take time off until after the baby was born. "I'm really going to kick back and wait and see when this baby is going to come, spend my time with my family and my wife," he said.
Spears vowed that after the birth of her second child she'd get back to the gym – and back to work. "I'm definitely going to start working out in a huge way," she told PEOPLE last month.
Plus, the singer, whose last original album was 2003's In the Zone, is working on a new album due next year, which she describes as "cooler than ever – fun, upbeat and sexy."
For info on how Spears got ready for baby No. 2, click here.