The Church has admitted failing to properly supervise Stephen Brooks, who carried out 19 assaults when he worked as a clergyman over a seven-year period.
Brooks, 62, was jailed in 1994 after admitting raping young boys in his home in Sketty.
The South Wales Evening Post has reported that one of the victims, now in his mid-30s, was too traumatised to give evidence against the vicar but he told police he was abused at St Paul's Church.
A civil case was launched by the man's solicitors 22 years after Brooks was jailed, who argued that the church was responsible to an extent for the assault's.
Solicitor, Dino Nocivelli said: "It was clear to me that Brooks had used his position as a priest to obtain access to my client before manipulating him and then sexually abusing him.
"I felt the church were, therefore, equally responsible for the abuse as they had failed to supervise Brooks even though they knew he had frequent interaction with young children as a direct result of his employment."
A settlement was agreed between The Church in Wales and the victim who was compensated £58,500.
Mr Nocivelli said: "This was a significant case for my client who not only finally felt the church had acknowledged the abuse but had also listened and had tried to appreciate how the abuse had impacted his life.
"Survivors of child abuse should no longer have to suffer in silence and this case proved to be very important to my client's aim to finally obtain closure and justice."
The survivor of abuse said that it has "ruined" much of his life and made him question his own faith after the church did not reach out to him following his abuser's trial.
The man said: "It has had a huge impact on my life and has caused me to have low self-confidence and self-esteem.
"This has caused me to have difficulties in personal relationships and I have never disclosed the abuse to a partner, apart from my current partner. But even she does not know the true extent of the abuse.
"The abuse ruined so much of my life, and I feel the church has also let me down as it should have stepped forward to apologise when Brooks was convicted for sexually assaulting us. The abuse has definitely dented my faith."
Brooks was sentenced to four years in jail at Swansea Crown Court and the judge said he "caused immense harm and anguish."
A spokesperson for the church said that it cannot comment on legal cases due to confidentiality.
But went on: "However, we stress that we deplore all abuse of children and vulnerable adults and we take safeguarding very seriously.
"We have robust procedures in place to deal with any allegations and have conducted a review of historic cases."
