Staff at the Mid Yorkshire Hospitals NHS Trust asked for help to track down the woman earlier this week, following the birth outside Pinderfields Hospital in Wakefield on Tuesday, July 10.
A Facebook post from the organisation was shared more than 1,000 times and within hours Janet Watson came forward.
The 58-year-old from Whitley, near Selby, had been at the hospital that morning and returned to her car with her sister to find a pregnant lady leant against it "absolutely screaming".
"We didn't have a clue what to do," Mrs Watson said, grateful when nurses Sharon Scattergood, Lucy Tuncay and Sally Jennians who had been alerted to a woman in labour in the car park, came to help.
Ms Scattergood said: "I saw a woman in advanced labour leaning on a car. There was another woman, who was the owner of the car, by her side and I assumed she was her friend or relative.
“I got the lady to lie down in the back of the car and by this time Lucy and Sally had also arrived. Lucy called 999 and Sally helped her with her breathing whilst I delivered the baby. By the time the lady’s partner came back with a wheelchair the baby had been born."
The baby was safely delivered and taken with her mum to the hospital's maternity unit where they were discharged later the same day.
It was only later that staff were made aware that the car belonged to a stranger.
Ms Scattergood said: “I never for one minute thought that she was a stranger to the pregnant lady, I can’t imagine what she must have thought when suddenly there was someone having a baby in the back of her car."
The trust wanted to track down Mrs Watson to reimburse her.
David Melia, Director of Nursing and Quality, said: “This was an amazing act of kindness by Janet, and we’re all so thankful to her. She has also declined all offers of reimbursement for the cleaning of her car, which further demonstrates what a wonderful person she is.
"We can’t let her act of kindness go unnoticed though and will be sending Janet an appreciation of our thanks.
“I’ve also thanked the three fabulous nurses who acted so quickly and safely delivered the baby. I never cease to be proud of the colleagues I work with.”
Mrs Watson said: "I think the lady had a 10lb baby with no pain killers! She did absolutely marvellous. That's all I was bothered about that mum and baby were okay."
She added: "I'm sure I only did what anyone else would have done if something like that happens."