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Ten members were voted onto the power-sharing executive in Stormont under the leadership of Unionist First Minister David Trimble.
Westminster will now be asked to approve an order devolving power to the Assembly, with actual power expected to be transferred on Thursday.
Later this week, the British and Irish Governments will implement constitutional changes laid down in the Good Friday Agreement.
The articles of the Irish Constitution that lay claim to Northern Ireland will be dropped, while the 1985 Anglo-Irish Agreement is to be superseded by a new British-Irish Agreement.
But the appointment of Sinn Fein's chief negotiator, Martin McGuinness, a suspected former IRA commander, as the minister in charge of Ulster's schools has provoked anger from some unionists.
Next to Gerry Adams, the Sinn Fein president, Mr McGuinness, is the most powerful member of the Republican movement and was once jailed in the Irish Republic for membership of the IRA.
While hard-liners in Reverend Ian Paisley's Democratic Unionist Party agreed to take their seats in the cross-community government three members walked out of the meeting on hearing Mr McGuiness's appointment.
Danny Kennedy, the Unionist chairman of the assembly's new education committee, said many parents, teachers and educationists would be "very concerned and alarmed" by the "deliberately provocative" appointment.
Despite the protests Mr McGuinness pledged to commit himself to "exclusively peaceful and democratic means", and to serving "all the people of Northern Ireland equally".
"In my opinion all of the children of this island, no matter what political persuasion they come from, are our most important natural resource.
"We have to nurture them, we have to care for them, we have to treat them with equality, treat them with justice and in the course of my work I will be working in a very co-operative fashion with parents and teachers to do our best for our children," he added.
In the share-out of executive posts Mr Trimble chose the enterprise, environment, arts and culture for his party.
But his deputy, John Taylor, distanced himself from the executive by declining a ministerial post.
John Hume, the Social Democratic and Labour Party leader, selected finance, agriculture and higher education for his party.
Seamus Mallon was re-instated as Deputy First Minister after a three-hour debate, while Rev Paisley's deputy, Peter Robinson, became minister for regional development and Nigel Dodds accepted the social development post.
Mr Hume said the successful nomination of ministers represented a "huge and historic development".
"This is the first time in our history that representatives of all sections of our people will be working together in government. It will transform our society and replace the politics and violence of the past," he added.
Despite the Democratic Unionist appointments, Mr Robinson and Mr Dodds still refused to sit down with Sinn Fein.
Other ministerial members voted onto the assembly included Brid Rogers (SDLP) as agriculture minister, Michael McGimplsey (UUP) as minister of culture, Sam Foster (UUP) as minister of the environment and Sean Farren (SDLP) became minister of higher and further education and employment.
The Good Friday Agreement was signed at Stormont in April 1998 to create the Northern Ireland Assembly and new cross-border institutions.
The assembly became fully operational when power was handed over from London on 2 December 1999. But it was dissolved several times over the issue of weapons decommissioning.
Failure to resolve the deadlock over decommissioning led to a return to direct rule on 12 February 2000.
Talks followed and when the Provisional IRA indicated that it would put its arms beyond use, the Assembly and the Executive were reconvened on 30 May 2000.
But David Trimble resigned as First Minister on 1 July 2001 over the decommissioning issue.
He was re-elected on 6 November 2001 after a deal was struck with the Alliance Party.
But less than a year later, in October 2002 London suspended the Northern Ireland Assembly once more over alleged intelligence gathering by republicans.
Mr Trimble stepped down as leader of the Ulster Unionists after the party lost all but one of its MPs in the 2005 election. In July 2005 the IRA announced it was laying down its weapons for good.
Devolved power was restored to the Assembly on 8 May 2007. DUP leader Ian Paisley and Sinn Fein's Martin McGuinness - age-old opponents - took office as first and deputy first ministers respectively ending five years of direct rule.
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