The four-day trip by President Michael D Higgins follows the queen's groundbreaking visit to Ireland in 2011, which helped put British-Irish relations on a new footing.
One of the highlights will be a royal banquet at Windsor Castle today evening attended by Northern Ireland Deputy First Minister Martin McGuinness, a former IRA commander.
Before leaving Ireland, Higgins said the challenge was not to "wipe the slate clean" of all the distrust and difficulties of the past, but to look to the future.
"My hope for the visit, at the end of it all, is that people will, in ever more numbers, come to share in experiencing the history, the present circumstances and culture."
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He added: "The challenge is to hand to a future generation all of the prospects of the future. You are not inviting them to an amnesia about any deep dispute."
The president was greeted in London by Prince Charles, the heir to the throne, followed by a ceremonial welcome by the 87-year-old queen and her husband Prince Philip at Windsor Castle, west of London.
It would once have been unthinkable for McGuinness to attend such an event, although the Sinn Fein politician has already met the queen. The pair shook hands in a highly symbolic moment in Belfast in June 2012.
As a commander of the Irish Republican Army (IRA), McGuinness had a prominent role in the bloody battle for Northern Ireland to be part of the Republic of Ireland to the south.
The province remained part of the United Kingdom when Ireland gained independence in 1922, and was a source of huge tension between Dublin and London.