The Fashion Star host and fiancé Eric Johnson welcomed daughter Maxwell Drew Johnson on May 1 in Los Angeles in a birthing suit which was rumoured to have cost $4,000 per day.
According to US Weekly, Simpson is recovering well and is "excited" about her baby's arrival.
"Jessica is doing great and really happy. She's feeling well and relieved the baby is healthy," a source told the publication.
"The family will be dedicating the rest of this week and most of next week to helping Jess recuperate and take care of the baby. Eric is super happy as well."
Another insider added: "Everyone is marvelling at what a natural Jessica is. She was born to be a mum!"
Simpson was recently rumoured to be considering selling photos of Maxwell to a weekly magazine.