He shared the prize later that year with the Protestant leader of the Ulster Unionist Party, David Trimble, for their efforts to end the sectarian violence that plagued the region for three decades and left more than 3,500 people dead.
The talks helped pave the way for a joint initiative by the British and Irish governments in 1993 that spawned a peace process and an IRA truce in 1994 - and ultimately paved the way for the watershed Good Friday accord four years later.
A book of condolence for Mr Hume was opened at Derry's Guildhall on Monday.
Mr Eastwood compared his predecessor to the famous United States civil rights leader Martin Luther King.
Born on January 18, 1937, in Northern Ireland's second city - Londonderry to British Unionists, Derry to Irish nationalists - Hume trained for the priesthood before becoming a fixture on Northern Ireland's political landscape.
Mr Clinton said: "Through his faith in principled compromise, and his ability to see his adversaries as human beings, John helped forge the peace that has held to this day".
John was heavily involved in the civil rights movement in Northern Ireland around the start of the Troubles and was elected to Stormont in 1969.
"When others were stuck in the ritual politics of condemnation, John Hume had the courage to take real risks for peace", Adams said in a statement.
"He was the greatest Irishman ever and he achieved something that no-one could ever achieve before him: he ended the Anglo-Irish conflict, the conflict that had gone on for 800 years, and he gave my generation the opportunity to achieve our political goals peacefully and democratically, and that is an enormous legacy". He was insistent it was possible, tireless in pursuit of it and endlessly creative in seeking ways of making it happen.
In Northern Ireland, tributes were led by First Minister Arlene Foster, who recalled a "giant in Irish nationalism". "In our darkest days he recognised that violence was the wrong path & worked steadfastly to promote democratic politics".
Deputy First Minister Michelle O'Neill described Mr Hume as a "huge political figure in our society for many decades".
"The life of John Hume will forever be a blessing upon this island since Ireland is now blessed by the peace he gifted to us all".
Tributes were also paid by the Irish rock band U2.
His frequent, nearly identical statements in the early 1990s about the importance of dialogue, peaceful means and - crucially - agreement, were much-mocked, even by friends, but the point was that it was an approach and an outlook that would eventually work. "The family drew great comfort in being with John again in the last days of his life", the statement continued.
Hume had been largely out of the public spotlight since resigning as leader of the SDLP in 2001, citing ill health.
Pat and John Hume.
The mayor of Derry and Strabane, Brian Tierney, said he was "a true son of Derry and a hero of Ireland", adding: "RIP Ireland's greatest".
"John was a husband, a father, a grandfather, a great-grandfather and a brother. He was very much loved, and his loss will be deeply felt by all his extended family".
His funeral Mass will take place in the cathedral at 11:30 on Wednesday.