Cherie Blair, a 45-year-old high-flying lawyer, her husband and the baby returned to Downing Street after the birth.
"Both mother and baby are doing well," the spokesman said.
"Both the Prime Minister and Mrs. Blair are delighted. The three have now returned to Downing Street."
The spokesman had no further details.
The baby came after a 12-year gap from the Blair's other three childrenEuan, 16, Nicky, 14, and Kathryn. He is the first to be born to a serving British prime minister in over 150 years.
News of the pregnancy took Cherieand the rest of the nationby surprise when it was announced last year.
After decades of much older occupants at No.10 Downing Street, the Blairs' arrival at the prime minister's residence with their children and assorted toys in tow was hailed as a breath of fresh air.
Cherie Blair, a Queens Counsel barrister, worked right up until the baby's birth. And the often thorny issue of combining career and family was at the center of her work.
She failed to persuade her husband to take parental leave after the birth of their baby. But in her last court appearance before the birth she challenged his government over its parental leave regulations.
Mrs. Blair argued that her huusband's Labour government was unlawfully excluding 2.7 million people who were already parents of children under five from taking time off work to be with their children.
"A parent is a parent for life," the heavily-pregnant Mrs. Blair said. Parental responsibilities were not just tied to the "magic birthdate," she said to smiles all around the courtroom.
But Blair has remained adamant that he will not take paternity leave, although he has promised to try to spend more time at home.
He also told The New York Times in a recent interview that he suspects the baby night duty would fall to him.
"Cherie has many excellent qualities, but once she goes to sleep, it takes a minor nuclear explosion to wake her up," he said.