Jessica and fianc Eric welcomed their first child together on 1 May, with the singer announcing her baby girl's arrival on her website:
"Eric and I are elated to announce the birth of our baby girl Maxwell Drew Johnson. We are so grateful for the love, support and prayers we have received. This has been the greatest experience of our lives."
Simpson is believed to be resting comfortably with baby Maxwell, who weighs 9 lbs 13 ounces.
Her sister Ashlee revealed her excitement to People magazine, gushing:
"Bronx [Ashlee's child] and I are in love with Maxwell already! Jessica has wanted to be a mum since we were little girls and I couldnt be more excited for her and Eric!"