Saturday's vote offered Northern Ireland "a second chance" to make the Belfast Agreement work, the Northern Secretary, Mr Peter Mandelson, said.
Speaking at Hillsborough Castle shortly after signing the order to end direct rule at midnight tonight, Mr Mandelson said: "Northern Ireland today has a second chance to get it right. It is incumbent on all of us to take that chance and finally implement all of the agreement the people voted for."
He complimented Mr Trimble and the leaders of all the Northern parties, saying they had shown great vision and great imagination.
"I know that this has been a very difficult and painful decision for unionists but, by the same token, it has been difficult and painful for republicans to produce the statement that they did." He said the party leaders had shown flexibility in how they had been prepared to "stretch" their constituencies during the peace process.
He added: "This is an opportunity to put the conflict, the violence and the threat of violence behind us."
It was put to Mr Mandelson that, with a steadily shrinking majority within his party, the victory had been a Pyrrhic one for Mr Trimble.
"The Ulster Unionist party now has to show a renewed sense of confidence," he said. "Instead of being locked in the past, it has got to look forward and go on to the front foot."
He denied that further private assurances about the retention of the title of the RUC had been given before the UUC vote. "I have not given, do not give and would not give undertakings in private that I would not make in public. My position on the Patten Report was set out in a statement to the House of Commons in January.
"I am not going to give any assurance or concession or anything else that goes beyond or exceeds what I said in the House of Commons." Mr Mandelson said he hoped that the DUP would also retake its seats in the Executive as "government, and politics, in Northern Ireland as a whole" would be the worse for its absence.
"They supplied two very effective Ministers and it would be a shame if those people in Northern Ireland who voted for the DUP on the basis that they would take up their seats were to have their participation in a devolved government denied them," he said.