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The decision is a result of a meeting Sinn Féin's ruling council held on Friday in Dublin to discuss the meeting of the Minister and the Queen when she visits Northern Ireland.
However the initial meeting and handshake betweeen is expected to take place in a private room at the beginning of the engagement, sources close to the planning have said.
"This will understandably cause difficulties for some republicans and nationalists," Sinn Féin President Gerry Adams said. "Especially for those folks who suffered at the hands of British forces."
Mr Adams defended the decision, saying: "We don't have to do it. We're doing it because it's the right thing to do, despite the fact that it will cause difficulties for our own folk.
"But it's good for Ireland. It's good for this process we're trying to develop. It's the right time and the right reason.
"After Martin McGuinness completes this engagement he will be as true, as staunch, as active a republican as he ever was."
The historic moment is expected to happen at a Co-operation Ireland event in Belfast for next Wednesday with the monarch and Irish President Michael D Higgins invited.
They are both joint patrons of the charity and are expected to attend alongside First Minister Peter Robinson and Mr McGuinness.
The deputy First Minister was attending an inter-governmental meeting in Scotland but had said his party's decision would be guided on what would be best for the peace process.
The charity's chief executive, former senior Northern Ireland police officer Peter Sheridan, said Wednesday's reception is an important step forward for the "healing process".
"It is something that demonstrates to ordinary people out there that we have gotten to the stage where we can acknowledge each other with respect. It does not mean that we have to agree," he said.
The Co-Operation Ireland event recognises the "transformational strength" of arts and culture across the island. It will take place at the Lyric Theatre in Belfast.
Today’s decision is the right thing to do at the right time and for the right reasons.
Owen Paterson, Secretary of State for Northern Ireland, said the Queen's visit to Ireland last year took relations between the two countries to a whole new level.
"There is already massive public excitement about Her Majesty's visit to Northern Ireland next week.
"It is right that The Queen should meet representatives from all parts of the community.
He concluded: "Today's news will ensure that next week's visit will move Northern Ireland a whole new step forward."
First Minister Peter Robinson confirmed he would be attending the Cooperation Ireland event on Wednesday.
The DUP minister said he was "glad" Mr McGuinness had also accepted the invitation.
"We recognise that this will be a difficult ask for Her Majesty The Queen and a significant step for republicans.
"The process has required us all to reach out and take decisions outside our comfort zone.
"It is the right decision and a step forward for Northern Ireland."
Meanwhile, former Cabinet minister Lord Tebbit, whose wife was paralysed in the 1984 Brighton bombing, said: "Personally, I think it is hopeful that Mr McGuinness has decided, presumably on behalf of Sinn Fein, that he should accept the sovereignty of the Queen over Northern Ireland.
"I hope it will be followed by some further moves to express repentance for violence that was caused by Sinn Fein-IRA."
The Tory peer continued: "We know the views of the people of Northern Ireland. They wish to remain within the UK, so hopefully Martin McGuinness now realises that what went on was violence without a point."
Elsewhere, an extra 2,000 free tickets were snapped up in minutes for the Queen's Diamond Jubilee celebration in the grounds of Stormont next Wednesday. The first round of 10,000 tickets were allocated in six minutes.