Bishop Mehaffey, who was 88, died on Monday evening surrounded by his family.
His funeral took place at 1.30 pm on Saturday at St Columb’s Cathedral.
Dr Mehaffey led the Diocese of Derry and Raphoe from September 1980 until his retirement in 2002.
During his time as bishop he officiated at the funerals of many parishioners killed in the Troubles.
Dr Mehaffey, who was born near Portadown, developed a close friendship with the late Catholic Bishop of Derry, Dr Edward Daly.
The two men released joint statements, took part in foreign trips together and jointly led carol services during some of the worst years of the Troubles.
Following his death, a book of condolence has been been opened at Derry’s Guildhall.