White’s family campaigned for more than a decade for the father and son to be allowed to meet.
They previously told the that he had been moved between 16 different prisons since 2012, when he was given an imprisonment for public protection (IPP) sentence.
The regular changes meant White had never been able to complete rehabilitation courses that would have been necessary for him to be granted parole, his family said.
They also said White had developed paranoid schizophrenia during his time in jail, which further frustrated efforts to get the authorities to agree to a meeting between him and his son.
The pair have been able to talk on the phone almost every day, but from now on Kayden will be allowed to see his father every month.
Ms Smith said for a long time White had been “trying to raise a child over the phone in the most awful conditions”.
She added: “The visit has give him hope but at the same time he feels hopeless – he knows he may never live a fruitful life with his son.”
IPP sentencing was mainly used for serious offenders, but it was also used for some repeat offenders guilty of less serious crimes until it was abolished in 2012.
The two-hour visit was granted after the former Home Secretary, David Blunkett, intervened in White’s case.
Lord Blunkett brought in IPP sentences during the Labour government of 1997 to 2010, but has since said he “got it wrong”.