The Queen's visit to the Republic of Ireland will "put a seal on the past and build for the future", former prime minister Sir John Major said.
Sir John, who first set in train the peace process in Northern Ireland which led to the current power-sharing arrangements, said that the visit was the most significant royal trip for many decades.
He dismissed the suggestion of Sinn Fein leader Gerry Adams that the visit was "premature" and said he did not anticipate that the Queen would deliver any apology for the UK's past involvement in Ireland.
Speaking to BBC2's Newsnight, Sir John said: "This (visit) puts the seal on a relationship that was sour and is no longer sour.
"It puts a seal on the past and builds for the future. I can't think of anything of equivalent significance in the last few decades."
And he added: "I think it will set a new mark for relations between the UK and Ireland."
Sir John said that the atmosphere of relations between London and Dublin had "changed beyond belief" over the past 20 years.
From a position in the early 1990s when the rare conversations between prime ministers of the two countries were "frosty", UK-Irish relations had now reached the point where they were close political allies and major trading partners with 200 flights a day between their airports and a high level of "interplay" between their populations, he said.
"The atmosphere has changed tremendously and I think the Queen's visit will be not reflecting on the past, but looking forward to an ongoing relationship," said Sir John.
Asked if Her Majesty should make any apologies during her visit, he replied: "I don't think the Queen is going there to look at the past at all and I don't anticipate that that will be the case.
"I think what the Queen is going there for is to do what she has consistently done since she became Queen, which is to look to the future."
It was "quite remarkable" that the Queen was making such a trip, when she had lost her close relation Lord Mountbatten to an IRA bomb, said Sir John, who was himself in Downing Street when the Republican terror group attacked it with mortars in 1991.
If Mr Adams regarded the trip as "premature", he should raise it with Irish President Mary McAleese, who invited the Queen to the Republic, said Sir John.
"I don't think it is remotely premature," he said. "I think it is entirely right to go now."
The visit was supported by "the overwhelming majority" of Irish people, though he accepted that some protest was likely.
"You can find people who will demonstrate against anything and anyone on any occasion," he said. "So I think there may well be a handful of people who demonstrate, but that plainly - from what we have seen in nine months of preparations - is not the view of the overwhelming majority of Irish people."