David Trimble died on Monday at the age of 77.
Following the death of the former Stormont first minister on Monday, Prime Minister Boris Johnson described him as a political “giant” whose achievements would never be forgotten.
Taoiseach Micheal Martin credited his “central contribution” in efforts to secure peace and reconciliation.
Irish President Michael D Higgins praised his “life of public service”.
Mr Johnson tweeted a tribute to Lord Trimble on Monday evening.
“He was a giant of British and international politics and will be long remembered for his intellect, personal bravery and fierce determination to change politics for the better,” he said.
Mr Martin said: “All of us in politics at the time witnessed his crucial and courageous role in the negotiations leading to the Good Friday Agreement and his leadership in building support in his party and his community for the Agreement.”
President Higgins expressed his deep sadness.
“David Trimble’s dedication and courage, often during the most challenging times, has earned him a distinguished and deserved place in our history books,” he said.
“His work leaves a true legacy on the necessity and value of peace on our shared island for future generations.”
Current UUP leader Doug Beattie described the former first minister as “a man of courage and vision”.
“He chose to grasp the opportunity for peace when it presented itself and sought to end the decades of violence that blighted his beloved Northern Ireland,” he said.
Labour leader Sir Keir Starmer tweeted: “Very sad news. David Trimble was a towering figure of Northern Ireland and British politics as one of the key authors of the Good Friday Agreement, the first First Minister and winner of the Nobel Peace Prize. My thoughts are with Lady Trimble and their family.”
Sinn Fein vice president Michelle O’Neill tweeted: “His very significant contribution to the peace process and his courage in helping achieve the Good Friday Agreement leaves a legacy a quarter century on for which he and his family should be rightly proud.”
DUP leader Sir Jeffrey Donaldson described the peer as a “committed and passionate advocate for the Union”, at a time when doing so posed a considerable threat to his safety.
Sir Jeffrey, who quit the UUP and defected to the DUP while Lord Trimble was leader, said: “Whilst our political paths parted within the Ulster Unionist Party, there can be no doubting his bravery and determination in leadership at that time. He was a committed and passionate unionist who always wanted the best for Northern Ireland.”
Alliance Leader Naomi Long said: “Lord Trimble’s greatest legacy to his political career is the Good Friday Agreement and the risks he took to both help achieve it, and ensuring the resulting Assembly remained during its unsteady early days. It was at times an unenviable role.
“His contribution to the peace process and the ending of violence in our society helped secure his place in history.”
SDLP leader Colum Eastwood said Lord Trimble had left an “indelible mark on our shared island’s story” and that without him there would not have been a Good Friday Agreement.
“Over the course of his political career but particularly in difficult years of the Good Friday Agreement negotiations he demonstrated immense courage and took political risks that sustained the life of our fledgling peace process,” he said.
“He doesn’t often enough get credit for it but without David Trimble’s fortitude, there would simply have been no agreement.”