The Queen and Mr McGuinness first shook hands privately at a cultural event organised by peace-building charity Cooperation Ireland in Belfast's Lyric theatre.
The pair shook hands for a second time - on camera this time - at the end of the engagement.
As Mr McGuinness held the Queen's hand for a few moments, he spoke to her in Irish and then explained that the words of farewell as she left the Lyric meant: "Goodbye and God Speed."
He later waved farewell to the Queen and Prince Phillip as the Royal car pulled away.
He also briefly told journalists the meeting "went really well", before joking: "I'm still a Republican".
Speaking outside the Dáil, Sinn Féin President Gerry Adams TD said the legacy of conflict had not been brought to a conclusion but that "all in all it's a good day for Ireland".
I think the vast majority of unionists will be pleased that this happened because they know it's essentially a real gesture beyond the rhetoric.
"I know that some people in the north - especially in my own home district of Ballymurphy - who are big supporters of the peace process are hurt," Mr Adams said.
"Just last week they were told by the British Secretary of State Owen Paterson that they would not have the type of inquiry that they were looking for, the kind of investigation that they wanted, into the deaths of their loved ones by the British Army."
He added the significance of the meeting "will be seen in how much we can build upon it".
Irish President Michael D Higgins, co-patron of Cooperation Ireland, said he was pleased to participate in the event.
He said the exchange "marks another important step on the journey to reconciliation on this island".
"I believe this will be very helpful in the continued realisation of the full potential of the Good Friday Agreement and in improving relationships between all communities who share this island," he said in a statement.
Northern Ireland Secretary of State Owen Paterson said that the meeting had gone "very well" and would move Northern Ireland onto a "whole new plane".
First Minister Peter Robinson said it was a "moment of history" but emphasised it wasn't the focus of the Queen's visit.
The focus has been on a handshake and a photograph but, for most people in Northern Ireland, it is not about one moment of history - but the opportunity to celebrate and give thanks for 60 very full years.
Peter Sheridan, from the Cooperation Ireland charity, said the moment was an example of peace-building.
He said of the mood: "It was a very relaxed atmosphere, the very ordinariness of it, even if it was not ordinary people."
Also present at the event was renowned poet Michael Longley, who said: "I think it's very significant. To dismiss this as theatrical is nonsense - a handshake is a handshake, no matter who you are.
"I think it carries on from her visit to the Republic and the fact that she met Mr McGuinness, who has made a huge contribution to the peace process, is very important."
Kate Carroll, widow of Constable Stephen Carroll who was killed by dissidents in 2009, said she found the meeting "uplifting" and "heart-warming".
"It just goes to show things are moving forward and that we're not going to be digressing, so I'm really happy with the outcome," she said.
"If we want this country to move on in leaps and bounds then this is the first way to do it. Forget old wounds and put everything else ahead. Don't go back, look forward."