President Higgins and his wife Sabina touched down at London Heathrow on Monday afternoon accompanied by the Tánaiste Eamon Gilmore.
They were met by the Viscount Henry Hood, Lord-in-Waiting, on behalf of The Queen. From there, they travelled to Windsor Castle where they will be based for the duration of their stay.
Speaking to the press earlier as he departed from Áras an Uachtaráin with full military honours including a Guard of Honour, President Higgins said the official meeting was a sign of the normalisation of relations between the two countries.
He said: "The peace process is that, it is a process that comes after the formal agreement at one level. Ultimately it is an exercise in consciousness at the level of community.
"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.
My wish is that Irish people and our neighbours come to visit each other more and it should be something that happens naturally, and I think it will happen
Michael D Higgins
"There are a lot of very difficult memories and it would be to my mind wrong to suggest to anyone that you should as it were, wipe the slate clean."
UTV's Political Correspondent Tracey Magee said the visit is the culmination of a long process.
She said: "We talk a lot about historical occasions during the peace process and this is very much another one. There has been a build-up in this relationship between the Irish government and UK government under Mary Robinson, Mary McAleese and now Michael D Higgins.
"This is the culmination of a lot of work to normalise, if you like, Anglo-Irish relationships - we saw The Queen's visit in 2011 and this is very much a reciprocal journey."
On Tuesday President Higgins and Mrs Higgins will be met by the Prince of Wales and the Duchess of Cornwall at the Irish Embassy.
They will then receive a ceremonial welcome at Windsor Castle where they will be formally greeted by the Queen and The Duke of Edinburgh. A state banquet in honour of their guest will be held that evening.
President Higgins and his wife were issued the invitation to stay at Windsor Castle by the Monarch last year.
Its significance was further deepened at the weekend as it was announced that the deputy First Minister Martin McGuinness will join Mr Higgins at the banquet.
On Sunday, Mr McGuinness, a former MP who refused to take his seat at Westminster, said he had accepted the invitation to send a "message to everybody about how things have changed".
When the Queen made a historic trip to Ireland in 2011, Mr McGuinness snubbed the gala banquet held in her honour at Dublin Castle.
But over a year later, the Queen and Mr McGuinness made history when they met and shook hands in Belfast's Lyric Theatre.
Mr McGuinness recently echoed the Queen's Dublin speech as he addressed an event in Warrington, at the invitation of the father of one of the 1993 IRA bombing victims.
Mr Higgins acknowledged the importance of the Queen's words about all those who lost lives in the conflict.
"I think Her Majesty in coming to Ireland and addressing for example issues of relations between our two people was doing it the right way," President Higgins commented.
"The words chosen and the symbolic way they were delivered by the Queen herself were extraordinarily important.
"The decision for example not to ignore the past but to address it, to go on and say as well, not only would things have been done differently but maybe not all, that was adding generosity to a kind of an ethic of memory."
Meanwhile the DUP MP Nigel Dodds welcomed the visit but added: "I think it's very much a reaction to the negativity which Sinn Féin received in the press and amongst the public about their boycott of The Queen's visit to the Irish Republic the last time.
"I think the very clear message coming from Sinn Féin in the south to the north is you'd better not mess it up this time."