Weighing in at 3.2kg and 57cm long, Alexander arrived in the world through a natural birth at a Los Angeles hospital, reports Life and Style Weekly.
Watts' rep said that the actress, who delivered 3:59 p.m. on July 25, was slightly ahead of schedule.
A source revealed that the couple had been expecting their child to be born in August, but had planned in case the baby came early.
"Naomi was planning on giving birth next week-- her due date was early August -- but since she insisted on delivering naturally, she knew there was a chance she would have the baby before the due date. That's what wound up happening," the publication quoted a source, as saying.
The insider added that both Schreiber and Watts were ecstatic over the new arrival.
"This is a dream come true for both of them and they've done everything in their power to make it as special as possible, right down to staying in the dark about the baby's sex right up until Naomi gave birth," the insider said.
Schreiber, 39, and Watts, 38, fell in love while shooting the romantic drama, The Painted Veil, in China in 2005.
Her pregnancy was inadvertently revealed by fashion giant Escada who designed her gown for this year's Oscars.
A spokesperson for Escada sent out a press release before this year's Academy Awards in which the fashion house stated that the ensemble created for her would offset her "most precious new asset".
"The Escada gown set off her most precious new asset - the baby she is expecting with longtime boyfriend Liev Schreiber," the rep said.