The President says Ireland and Britain now has the opportunity to advance our overlapping ambitions and shared hopes.
In the first ever address by an Irish Head of State to a joint session of the Houses of Parliament in Westminster, Michael D. Higgins says the relationship between the two islands is one of a closeness and warmth that once seemed unachievable.
In his speech Mr. Higgins referred to the passing of the Home Rule Act in the House of Commons and the election in 1918 of Constance Markiewicz.
The President says the two countries can take great pride in the progress of the cause of peace in the North - a road still to be travelled he says, one of lasting and creative reconciliation.
Michael D. Higgins recognised the visit by the Queen to Ireland three years ago and expressed how far we have come in understanding and respecting each other.
He says the ties between us are strong and resolute in trade, tourism, sport, culture and people to people connections.
The Irish community in the UK got special mention, with the President saying he greatly cherishes them and their contribution.
The President says there is now an opportunity to sketch our shared hopes and advance our overlapping ambitions.
Earlier, the President and Mrs. Sabina Higgins met Queen Elizabeth II and her husband, Prince Philip. Both the Irish and British national anthems were played on arrival at Windsor Castle.
They all travelled together by horse-drawn carriage for a ceremonial welcome.
In the Quadrangle at Windsor, the President inspected a Guard of Honour.
Then after a private lunch hosted by Queen Elizabeth II, she and the President viewed Irish related items from the Royal Collection.
Afterwards they departed for London and a visit Westminster Abbey. Prior to commencing a tour of the Abbey, the President lay a wreath at the Grave of the Unknown Warrior.
See the visit In Pictures here
Earlier, the Prince of Wales and Duchess of Cornwall were at the Irish embassy in London to meet President Higgins and his wife.
The Taoiseach has said this is a "very historic" day for the country. Enda Kenny said it is a particularly proud day for the Irish community in Britain.
The Sinn Féin Deputy President says the State Visit is a symbol of progress in Anglo-Irish relations.
The party opposed the visit by the British monarch to Ireland in 2011 but support President Higgins' return trip to Britain.
Mary-Lou McDonald says the peace process has led to this historic occasion but there is still much work to do.
While former Taoiseach Bertie Ahern says he can understand the concerns of those who object to Martin McGuinness attending a State Banquet tonight at Windsor Castle.
It was confirmed on Sunday that the North's Deputy First Minister would attend the event. The Tanaiste welcomed the news as a 'significant development'.
These people at Windsor Castle are showing their colours
Speaking to BBC Radio 5 Live this morning, Bertie Ahern had a message for those whose lives were affected by the Troubles in the north and are unhappy at Martin McGuinness' presence this evening.
Crowds gathered on the streets in Windsor for the ceremonial welcome. These people say the State visit is a momentous occasion.
While the visit is attracting plenty of attention among the media and at a political level, the British public is understood to have very little awareness of it.
Channel 4 news anchor Jon Snow says that is because people there are so used to crossing between the two countries and because Irish history is not taught in schools, so there is no real significance being attached to the event.
Jon Snow told Newtalk Breakfast the President is a remarkable figure, who will inspire British people.
