Sussex Police said a 67-year-old man, believed to be retired Reverend Vickery House, was also released.
Sussex Police said a man arrested this morning, believed to be retired Peter Ball, 80, a former Bishop of Lewes, was released this afternoon on medical advice:
The Bishop of Chichester, Martin Warner, confirmed an 80-year-old retired bishop and a 67-year-old retired priest were arrested this morning relating to "allegations of sexual abuse in the 1980s and 1990s".
The bishop said:
Today's arrests result from a review and subsequent investigation over the past six months into the scandal-hit Diocese of Chichester, Sussex Police said.
"This is a very complex enquiry, in the course of which many people, all now adults, have had to be traced, together with other witnesses and records from a wide variety of sources", the force said in a statement.
Police said there were no allegations of recent or current offending, and no suggestion that any young people are at risk.
They also said the claims are being treated separately and do not involve allegations the two men acted together.
A retired Church of England bishop was among two clergymen arrested by Sussex Police investigating historic allegations of child sex abuse within the scandal-hit Diocese of Chichester, according to sources.
Peter Ball, 80, was arrested at his home near Landport, Somerset, on suspicion of eight sexual offences committed against boys and young men during the late 1980s and late 1990s, sources said.
A second man, aged 67, was also arrested this morning at his home near Haywards Heath, West Sussex, on suspicion of separate sexual offences against two teenage boys in East Sussex between 1981 and 1983.
Sussex Police confirmed arrests have been made but did not reveal the identity of the suspects.
They are currently detained - in Somerset and Sussex respectively - for interviews by Sussex Police officers, the force said.
Peter Ball, a retired Church of England bishop, was one of two men arrested by Sussex Police over historic child sex abuse allegations, sources said.