A delighted President Clinton hailed the UUC decision to return to the power-sharing Executive as a "giant step towards fulfilment of the historic promise of the Good Friday accord".
The restoration of the institutions has revived speculation that the President will make a third visit to Northern Ireland before he leaves office early next year.
In his statement, Mr Clinton said he was "delighted" the Northern Ireland peace process was back on track.
"I congratulate David Trimble and the Ulster Unionist Council on their decision to return to self-government in Northern Ireland. This is a giant step towards fulfilment of the historic promise of the Good Friday accord: to provide self-government to all the people, on the basis of equality, consent and the use of exclusively peaceful means.
"The parties are now ready to re-enter the Executive and Legislative Assembly in the coming days. It is now possible for the politics of conflict to be transformed into the politics of consensus. I applaud the leadership of Tony Blair, Bertie Ahern and all the parties."
Senator Edward Kennedy welcomed the vote as "an important step forward in the effort to implement the Good Friday agreement". There is still anger in the White House at the article in the Guardian newspaper last week claiming Mr Clinton twice rebuffed appeals from Mr Blair to put pressure on the Irish Government and Sinn Fein to secure a compromise on the change of name for the RUC.
Denying the report as "total, complete fiction," the President's national security adviser, Mr Sandy Berger, said there had been "quite extraordinary co-operation" between Mr Clinton, Mr Blair and Mr Ahern.