Micheál Martin joined the President of the European Parliament, Roberta Metsola, to unveil the bust.
Mr Hume, a founding member of the SDLP, was one of the highest-profile politicians in Northern Ireland. He died in Derry in 2020.
The former MEP was also a key architect of the Good Friday Agreement in 1998.
The sculpture, one of four created by Irish artist Liz O’Kane, has been donated to the European Parliament by the Irish government.
It was installed in the parliament’s new members’ lounge on Tuesday.
Mr Hume’s son, John Hume Jr, said the unveiling of the statue was a very emotional occasion for their family.
“This building and what it represents meant a great deal to my father,” he said.
“He was an MEP here for over 25 years, and there is a great deal of symbolism to see him, in a way, become a permanent fixture within these walls.”
Mr Hume said the statue depicted his father when he was 40 years old, when he first became an MEP.
Chairperson of the Hume Foundation Dr Sean Farren said the installation of the bust at the European Parliament was “a very important moment for the Hume family”.
He said the European Union had inspired Mr Hume’s “journey of peace, reconciliation and diversity”.
“John Hume believed that respect for difference was the first principle of European Union. His powerful words resonant as strong today, as the people of Ukraine suffer from the violence of others,” he said.
Dr Farren added: “In the face of adversity we must continue to choose the way of peace and step back from the shadow of war”.
Two of artist Liz O’Kane’s sculptures of Mr Hume are housed in the Irish embassies in Washington and London.
The fourth is expected to be installed at the Department of Foreign Affairs in Dublin later this year.
Colum Eastwood, the current SDLP leader, said the sculpture was a “fitting tribute to an exceptional peacemaker”.
“John and Pat Hume’s influence and beliefs stretch out from Derry to everyone around the world,” he continued.
During his two-day trip to Strasbourg, Mr Martin will also meet representatives of the Council of Europe to mark Ireland’s presidency of the body from May to November 2022.
Later today the Taoiseach will address the European Parliament, reflecting on 50 years since Ireland decided to join the European Union.
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