From Galway, Murphy's first successful play, A Whistle in the Dark, was performed at the Theatre Royal Stratford East in London in 1961 and caused considerable controversy.
He worked closely with the Abbey Theatre and the Druid Theatre Company and he was hailed as a master of language by critics.
"It was with great sadness that Sabina and I have learned of the death of Tom Murphy," President Higgins stated this morning.
"The importance of Tom Murphy’s contribution to Irish theatre is immeasurable and outstanding. We have had no greater use of language for the stage than in the body of work produced by Tom Murphy since his earliest work in the 1960s.
"His themes were not only those which had influenced the very essence of Irishness, immigration, famine and loss - they were universal in their reach.
President Higgins added: "From the early beginnings of his writings in Tuam, Tom Murphy produced a unique and often provocative body of work. He was above all the great playwright of the emigrant, more than anyone capturing, in a poignant, creative way, the transience that is at the heart of the emigrant experience.
President Higgins also recalled his many meetings with the playwright.
"It was such a joy to meet Tom so many times over the years, and a particular pleasure for any of us who have been privileged to call him our friend," the president recalled.
"I had the pleasure of presenting Tom with the Aosdána torc in his home in 2017, a great acknowledgement by his contemporaries of his outstanding abilities as a writer.
"Sabina and I wish to express our condolences to his wife Jane and to Mary, Bennan, Johnny, Nell and their extended family and his wide circle of friends. I will miss him deeply, but he will be fondly missed by all of us who had the privilege of knowing him."