Mrs Keep, a pub cook from Redditch in Worcestershire, gave birth to the children in March after meeting the adoptive parents - Anthony and Julie Cohn - through an agency for childless parents.
Two eggs, fertilised by Mr Cohn, were taken from his wife, who was born without a womb, and implanted in Mrs Keep. The surrogate mother produced male twins from one egg and another brother from the second. The babies were born prematurely, weighing just 3lbs each but are expected to leave hospital in the next few days.
It was reported that Mrs Keep had refused payment for her role in the birth. She claimed she would do the same thing again.
"I wanted Anthony and Julie to feel the same overwhelming pride I did when I held my own first son 23 years ago," she was reported as saying.
"The happiness on their faces when they saw the babies for the first time made all the trauma worthwhile."