Gormley is the scupltor who designed the famous Angel of the North at Gateshead in northern England.
The "planting" of "Tree" marks the first event of the inaugural Happy Days Enniskillen International Beckett Festival, which takes place in the island town, from August 23 to August 27.
"Tree for Waiting for Godot" is a festival commission as part of a stage set for a future production of Samuel Beckett's most famous play Waiting For Godot.
The "flat-pack" sculpture has been made in 37 separate square stainless steel sections to facilitate theatrical tourability, and measures 2.9 x 2.8 x 2.9 metres.
Sean Doran, Founder and Artistic Director of the Happy Days International Festival said: "We are delighted that Antony has allowed "Tree for Waiting for Godot" to be exhibited for the first time at our inaugural Happy Days festival.
"With less than six weeks to go, it is an appropriate international symbol with which to kick-start the festivities. Waiting for Godot is Beckett's most famous work, known all over the world, and the sculpture will form part of a stage-set for a future Aboriginal-Australian and Irish co-production of the play".
Speaking on BBC Radio 4's Front Row, Gormley said he had corresponded with Beckett and sent him his first piece of work, "Fruits of the Earth", made from his father's First World War handgun: "I think of [Beckett] as a sort of father figure, because he understood the placement his stage directions for his plays were so absolute and so utterly aware of the critical factor of making a relational field. He made a roadmap for all creative minds to concentrate their effort".
"Tree" will remain at Castle Coole for 60 days to mark the 60th anniversary celebrations of the National Trust at Castle Coole.
The festival programme will present a diverse mix of international theatre, music, art, comedy and conversation from world class Irish, UK and international artists and writers.
The full programme is now on sale and tickets are available from www.happy-days-enniskillen.co.uk.