Simpson and her former football player fiance Eric Johnson announced Maxwell's arrival on her website.
"We are so grateful for all the love, support and prayers we have received. This has been the greatest experience of our lives," the couple said.
Simpson, 31, and Johnson, 32, became engaged in November 2010, but have yet to set a wedding date.
Simpson rose to fame as a teen pop star and became a household name after starring in a TV reality show with then new husband Nick Lachey, a member of the boy band 98 Degrees. The pair divorced after three years of marriage.
She went on to star in the 2005 film version of The Dukes of Hazzard and re-invented herself as a country singer in 2008. She currently designs apparel, accessories and other fashion products and is a mentor on the TV contest Fashion Star.
Johnson is a former US professional football player whose career spanned seven seasons.