But after being recognised as the infant's "private foster carers", the couple have been denied the chance to officially adopt her because they are too old.
"We both love (the little girl) and would be heartbroken to lose her," said the husband.
"They (the council) say they are putting her interests first, but she is so happy here with us."
The couple, who cannot be named for legal reasons, are aged 53 and 59, and want to remain long-term carers for the child, who is now 13 months old.
However, Reading Borough Council, in Berkshire, is opposing them and wants to persuade the family court to allow the child to be adopted by another couple.
The couple, who have raised five children, were contacted by a friend of their youngest daughter, begging for their help.
The 17-year-old mother asked them to look after her then three-and-a-half month old baby girl "for a while".
They spent their savings buying equipment for her care and saw the girl's weight and health increase as she was cared for.
At two adjourned hearings the council opposed their applications to continue to be allowed to foster the little girl.
At the second hearing the baby's natural mother and father both gave evidence asking the court not to allow the adoption to go ahead, but to leave their daughter with the Whitley couple.
The 59-year-old woman, who has asthma, said: "They say that we are too old - that with my health it will not be long before [the baby girl] becomes my carer.
"They say that we will be an embarrassment to her at school because we will be so old.
But half the kids are collected from school by their grandparents. And if we were her grandparents we would be allowed to adopt despite our age.
The natural mum did not get back in touch with the couple until shortly before Christmas but the dad - whose DNA test to prove fatherhood was actually paid for by the couple - has been regularly involved with his daughter with the encouragement of the couple.
RBC spokesman Oscar Mortali told the Daily Mail: "The council cannot comment on the individual detail of this case, but we fully understand how traumatic it can be for temporary carers to see a child they have cared for over a period of time possibly moving on to a permanent home.
"However, the council's absolute priority in any fostering or adoption case is to try and ensure the best long term future for children. That is also the case in this instance.
"Ultimately, it is for the court to decide on the final plan for the child based on the evidence presented to them from a range of people."
There is no upper age limit for adoption, but the carers must demonstrate they are healthy and have the necessary commitment and energy to bring up a child.The case has been adjourned until February 18 with a full hearing set for three days in mid-March, by which time the couple will have been looking after the little girl for a year.