Fassbach said doctors were being especially cautious "now that she's going into the world".
Amilliahas been in an incubator since she was born on October 24: "Even though she's only four pounds now, she's plump to me," Sonja Taylor, the baby's mother, said.
'All ready'
Confirming that baby Amillia was going home, Liz Latta, a hospital spokeswoman said: "The baby is healthy and thriving and left Baptist Children's hospital today after four months in our neonatal intensive care unit". 
"We're delighted," said Amillia's mother Sonja."They called me first thing this morning to let me know."
She will still need oxygen at home and a specialist will work with her parents to track her neurological development.
Amillia's father Eddie said: "We have that all ready".
'Uncharted waters'
Baby Amillia has suffered respiratory and digestive problems, as well as a mild brain haemorrhage, but doctors believe there will not be any major long-term concerns.
Another doctor who cared for baby Amillia, William Smalling said: "She's truly a miracle baby".
The neonatologist described caring for her over the past months as like navigating uncharted waters: "We didn't even know what a normal blood pressure is for a baby this small," he said.
Doctors say she is the world's smallest prematurely born baby and the first baby known to have survived after a gestation of fewer than 23 weeks.
Full-term births come after 37 to 40 weeks, and the American Academy of Paediatrics does not consider a foetus to be viable at less than 23 weeks.