The baby's name is Maxwell Drew Johnson. They plan to call her "Maxi."
Little Maxi weighed in at 9 lbs. 13 ounces, according to the magazine.
This is Simpson and Johnson's first child.
The "Fashion Star" mentor has spoken rather candidly about the not-so-pretty parts of her pregnancy.
She told Jay Leno that she started calling herself 'Swamp A**,' referring to the fact that she sweated through her Spanx.
Simpson also told Jimmy Kimmel that her belly was weighing so heavily on her "hoo-ha" that her water breaking would be "like a fire hydrant."
Simpson, 31, and Johnson, 32, got engaged in November 2010, but have yet to set a wedding date.
The pair has said they planned to walk down the aisle after their baby's arrival.
Simpson was previously married to singer Nick Lachey from 2002 to 2005.
Their marriage was chronicled in the MTV reality show Newlyweds."