He said he was "frankly appalled by the way the Church authorities have treated his memory".
In October 2015 the Church of England released a statement apologising to a woman who claimed she was abused by the respected Bishop Bell in the late 1940s and early 1950s.
It also paid compensation to the woman who cannot be named for legal reasons.
Sussex Police has revealed it would have arrested Bishop Bell and interviewed him on suspicion of serious sexual offences had he still been alive.
In a letter to Bishop Bell's niece Lord Carey is highly critical of the Church's response to the allegations.
"[I am] frankly appalled by the way the Church authorities have treated his memory," he said.
"Your uncle was a man whose contribution to this country and the Church was outstanding.
"He was without question one of the greatest Church leaders of the 20th Century.
"The Church has effectively delivered a 'guilty' verdict without anything resembling a fair and open trial.
"His reputation is in tatters and, as you sadly point out, all references to him in the diocese he loved and served have been removed and renamed."
The letter from Lord Carey, who was Archbishop between 1991 and 2002, has been published in the Mail on Sunday.
The newspaper said he wanted a public inquiry into the matter.
A Church of England spokesperson said: "Where allegations are made against a deceased person, as is the case with Bishop Bell, they must - of course - be taken seriously and dealt with accordingly, however uncomfortable this may prove, or however high profile the individual may be.
"The process leading up to the settlement, the apology and the announcement was long, complex and carried out with all the sensitivity that a case of this nature demands.
"The survivor who has chosen to remain anonymous, has since given an interview about her experiences and we acknowledge her courage in doing this."