The hospital said Amillia Taylor, who spent less than 22 weeks in the womb, was "healthy and thriving".
Amillia had been expected to leave on Tuesday but a low white blood cell count kept her in for more checks.
She measured just 9.5in (241mm) at birth. Babies under 14 ounces were thought to be unable to survive.
Mother Sonja Taylor said: "We are delighted... they called me first thing this morning to let me know."
Father Eddie said the oxygen tanks that Amillia would need at home were "all ready".
Hospital spokeswoman Liz Latta said: "The baby is healthy and thriving and left Baptist Children's Hospital today after four months in our neonatal intensive care unit."
Amillia, the Taylors' first child, had suffered respiratory, digestive and haemorrhaging problems but doctors said they believed she was now doing well.
Amillia's time in the womb is a record according to the University of Iowa which keeps track of premature babies born throughout the world.
"She's truly a miracle baby, " said Dr William Smalling, neo-natal expert at the Baptist Children's Hospital.
"We weren't too optimistic. But she proved us all wrong," he said.
Her parents named her Amillia - which means resilient in Latin, a fighter and hardworking - to reflect her survival against the odds.
Mrs Taylor said the worst thing had been not being able to hold her baby for more than six weeks after she was born.
Amillia's survival demonstrates the dramatic advances in neo-natal care in recent years, correspondents say.Güncelleme Tarihi: 20 Eylül 2018, 18:16