Farhat was born in Ain Kfaa, Lebanon, on 20 May 1933. On 28 March 1959, the Maronite Patriarch of Antioch Paul Peter Meouchi ordained him a priest. He earned degrees in theology, philosophy and canon law in Paris and Rome and a doctorate in theology.
On 26 August 1989, Pope John Paul II appointed him Apostolic Delegate to Libya, Apostolic Pro-Nuncio to Tunisia and Algeria, and titular archbishop of Byblus. On 20 October 1989 Farhat was consecrated a bishop by Pope John Paul. His co-consecrators were Edward Cassidy and Francesco Colasuonno. On 26 July 1995, he was named Nuncio to Slovenia and Macedonia.
He worked as mediator of diplomatic relations between the Sovereign Military Order of Malta and Macedonia, which thus the Order officially recognized. On 11 December 2001 he was named nuncio to Turkmenistan and Turkey. In Turkey his advocacy for Turkish membership in the European Union resulted in warnings that he was failing to comply with Turkish law limited the role of religion in civic affairs.
On 26 July 2005 he was appointed apostolic nuncio to Austria.
On 14 January 2009, Pope Benedict XVI accepted Farhat's resignation as Apostolic Nuncio to Austria. On 22 December 2009, Pope Benedict named him a member of the Congregation for the Causes of Saints.
He died in Rome on 17 December 2016.
- Honorary conventual of the Sovereign Military Order of Malta
- Grand Officer of the Order of Merit of the Italian Republic (2008)
- Decoration of Honour for Services to the Republic of Austria (2009)
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- "Rinunce e Nomine, 14.01.2009" (Press release) (in Italian). Holy See Press Office. 14 January 2009. Retrieved 6 August 2019.
- "Rinunce e Nomine, 22.12.2009" (Press release) (in Italian). Holy See Press Office. 22 December 2009. Retrieved 6 August 2019.
- Noun, Fady (30 January 2017). "In memory of Mgr Edmond Farhat, a bridge between the Vatican and the Islamic world". AsiaNews. Retrieved 6 August 2019.