Lord Carey resigned after allegations he allowed a priest, who had been banned over sexual abuse claims, to return to priesthood. However, the 89-year-old mentioned his age when announcing his decision to stand down.
The former archbishop of Canterbury has quit as a priest after an investigation into the Church of England's handling of a sexual abuse case.
George Carey resigned after the BBC contacted him about allegations he allowed a priest, who had been banned over sexual abuse claims, to return to priesthood.
However, Lord Carey, 89, mentioned his age when announcing his decision to stand down.
In his resignation letter, sent to the Diocese of Oxford on 4 December, he said: "I wish to surrender my Permission to Officiate.
"I am in my ninetieth year now and have been in active ministry since 1962 when I was made Deacon and then Priested in 1963.
"It has been an honour to serve in the dioceses of London, Southwell, Durham, Bristol, Bath and Wells, Canterbury and finally Oxford.
"I give thanks to God for his enduring faithfulness but want to recognise the remarkable contribution of [my wife] Eileen whose faithfulness and support has been outstanding."
'Some trepidation'
It comes after the Archbishop of York Stephen Cottrell faced calls to resign over claims he let David Tudor stay in post in the diocese despite knowing he had been banned from ministry for life earlier this year after admitting what the church described as serious sexual abuse involving two girls aged 15 and 16.
The archbishop said he was "deeply sorry that we were not able to take action earlier" over the sex abuse case.
In 1988 Tudor had been suspended from ministry for five years after admitting, according to a tribunal document, to having sex with a 16-year-old girl he met while she was a pupil at a school where he was chaplain - but he was later able to return to working in the church in 1994.
His return to the priesthood was helped by then-archbishop of Canterbury Lord Carey, according to the BBC.
It said in 1993 he agreed Tudor could come back under supervision in the following year - a move that was done "with some trepidation," the Church of England told the broadcaster.
Tudor was banned from ministry for life by a Church tribunal in October this year after admitting sexual misconduct.
Lord Carey was archbishop of Canterbury from 1991-2002.
During his time in office, he took part in the funeral of Diana, Prince of Wales and became the first archbishop to ordain women to the priesthood.
Lord Carey's spokesperson declined to comment on the BBC investigation.