Us Weekly confirmed that "Birdie" is indeed Simpson's daughter's name.
The songstress and her second husband Eric Johnson are already parents to Maxwell, six, and Ace, five.
The couple are overjoyed to be adding to the brood.
A pal dished, "Eric has been incredibly supportive and loving," says the source. "He is always right next to Jessica trying to help her with whatever she might need. He is also a super dad and Maxwell and Ace just adore him."