The star and her fiancé Eric Johnson welcomed daughter Maxwell Drew Johnson on May 1, she announced on her website.
"Eric and I are elated to announce the birth of our baby girl, Maxwell Drew Johnson," she wrote. "We are grateful for all the love, support and prayers we have received. This has been the greatest experience of our lives!!"
The baby weighed in at 9 lbs. 13 oz. and is 21¾ inches long. Maxwell is Johnson's middle name, while Drew is Simpson's mother Tina's maiden name.
Simpson announced her pregnancy on Halloween, posting a picture of herself on Twitter dressed as a mummy and cradling her belly. "It's true – I'm going to be a mummy," she wrote.
In March, she shared the news that a baby girl was on the way as she posed nude on the cover of ELLE. Weeks later, Simpson celebrated her baby shower.
Maxwell is the first child for Simpson, 31, and Johnson, 32, who had a whirlwind romance. The singer and the former NFL player started dating on May 2010 and were engaged six months later.