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David Trimble received a letter from Sir Tony Blair shortly before he died saying he had "changed lives for the better" through the Good Friday Agreement, the former PM has said.
Sir Tony told BBC News NI he wanted to tell the peer how important his role in the 1998 peace deal was.
He said his actions during the peace process were what "defines leadership".
Lord Trimble led the UUP from 1995 to 2005 and was the first person to serve as first minister of Northern Ireland.
Politicians from across the political divide are expected to attend his funeral in Lisburn, County Antrim, on Monday afternoon.
Senior representatives from the British and Irish governments, as well as a wide range of local politicians, are expected at the service.
He died on 25 July at the Ulster Hospital near Belfast, after a short illness.
Speaking to the BBC's Good Morning Ulster programme, Sir Tony outlined the contents of his last letter to the dying peer, which was written because Lord Trimble was too ill to take a phone call.
He praised Lord Trimble's leadership through the "agonising negotiations" which led to the Good Friday Agreement, saying he had set an important example for current political leaders.
Also known as the Belfast Agreement, the deal helped to bring an end to more than 30 years of violence in Northern Ireland, known as the Troubles.
Lord Trimble was jointly awarded the Nobel Peace Prize for his efforts, alongside the late John Hume, the then leader of the Social Democratic and Labour Party (SDLP).
However, many unionists opposed the agreement which allowed paramilitary prisoners to be released from jail without serving their full sentences.
"The toughest thing is always to say to the people who support you that 'I've got to take you in a new direction, I've got to do something different'," the former prime minister said.
"Because the easiest thing always to do with your own supporters is, frankly, to play the tunes they want to hear and to be prepared to introduce what to them, to many of them, is a discordant note.
"That takes a lot, but it is what defines leadership in the end."
Analysis: A changed landscape
By Mark Simpson, BBC correspondent
Many of the key politicians from the Good Friday Agreement era have passed away in recent years.
The historic deal in 1998 would not have been possible without David Trimble.
That is one of the reasons why politicians from many different political perspectives will come together under one roof to pay tribute to him.
Lord Trimble was awarded the Nobel Peace Prize in 1998 along with the then SDLP leader John Hume. Within the past two years, both men have died.
In recent years, Sinn Féin's Martin McGuinness, the SDLP's Seamus Mallon and the DUP's Ian Paisley have also passed away.
The political agenda in 2022 has changed.
Yes, there are still crises, but the main issues are no longer about life and death.
Lord Trimble, a former law professor, faced down strong opposition from colleagues within his own party in order to sign the Good Friday Agreement 24 years ago.
The deal led to the setting up of a new devolved government at Stormont and ushered in a new, more peaceful era of power-sharing politics.
But critics opposed his decision to form a ruling executive which included Sinn Féin ministers in advance of the IRA agreeing to put its weapons beyond use.
Unionist concern over the lack of IRA decommissioning ultimately cost him his job as UUP leader - he lost his Westminster seat to the Democratic Unionist Party (DUP) in 2005.
In his interview, Sir Tony said Lord Trimble was prepared to defend the Good Friday Agreement, even though he knew there would be a high personal cost.
"David said to me when we concluded it: 'Ok I'm going to go with this and once I give you my word, I'll keep it,'" Sir Tony said.
"He did say: 'It's going to cause a lot of angst and anxiety and a lot of criticism for me in doing it.' But he said: 'Nonetheless, I think it's right and we will go for it'."
Sir Tony described Lord Trimble as a very intelligent man with a very dry wit.
He recalled sitting with the then UUP leader in Downing Street, awaiting the arrival of Sinn Féin's Gerry Adams, when Lord Trimble spied a biography of Oliver Cromwell on a bookshelf.
Lord Trimble picked up the book and Sir Tony said: "I think he'd got it out just to make a dig.
"I said: 'I think we'll put that away before our next guest comes in.' So you know, he actually did have a real sense of humour."
Sir Reg Empey succeeded Lord Trimble as UUP leader in 2005.
Speaking ahead of the funeral, he said that Lord Trimble not only changed politics, he saved lives.
"There are many people, thank God, walking around Northern Ireland today who in my opinion would have been in their graves today if it were not for the decisions that he took," said Sir Reg.
In a family death notice, he was remembered as a "dearly loved husband of Daphne, and loving father to Richard, Victoria, Nicholas and Sarah".
Lord Trimble's funeral will be streamed on the BBC News NI website
You can listen to the full interview with Sir Tony on BBC Radio Ulster after 08:00 this morning.