The move by Sinn Féin to adopt a new policy supporting the PSNI has received a broad welcome.
Taoiseach Bertie Ahern hailed the vote as a 'landmark decision'
Taoiseach Bertie Ahern said the vote was a "landmark decision" which he said had opened the way to Northern Ireland power-sharing.
"It is vital that we continue to maintain the momentum from the St Andrews agreement and the timetable set out in that agreement," he said.
A spokesman for British Prime Minister Tony Blair said: "The Prime Minister welcomes this historic decision and recognises the leadership it has taken to get to this point."
Secretary of State for Northern Ireland Peter Hain said the vote was a "breakthrough" which had "put Northern Ireland in a place it has never been before."
"What had always been a massive impediment to stable and lasting government has been removed."
"We have always said that to make the breakthrough both Sinn Féin and the DUP have both to deliver on the twin pillars of support for policing and power-sharing. Now, that can be done."
He said it was time for all politicians to seize the initiative and close the deal that will bring devolved government back to the people of Northern Ireland.
Deputy leader of the DUP Peter Robinson said the move was to be welcomed but had to be supported by "delivery."
Mr Robinson said for the DUP to enter in a powersharing arrangement, "support for the police, the judiciary and the rule of law "is a necessary prerequisite."
"Sinn Féin having taken a decision in principle, which is to be welcomed, must implement that decision - and that is the basis on which we can move forward."
He added "the next step is theirs, the pressure is still on republicans."
The SDLP's policing spokesman Alec Attwood said the move should be welcomed and that "at long last Sinn Fein has moved past the redlight of policing."
UUP leader Sir Reg Empey described the vote as "the inevitable outworking of the peace process."
"Nonetheless today's move is a massive step change in the Republican psyche. It is an admission that the violent 'cause' has been abandoned and that Sinn Féin are prepared to support the forces of law and order in this part of the United Kingdom"
"My sense is that it could potentially herald the beginning of a new era if the follow through is clear, swift and unequivocal...Today's vote is a critical piece of the jigsaw in getting the much needed devolved institutions back up and running," he added.
However, Democratic Unionist MP Rev William McCrea dismissed the conference as "pantomime" and again cast doubt on whether republicans could prove their support for the police was for real by March 26.
"This has been a carefully choreographed move by them," the South Antrim MP said. "The fact remains that March 26 is not a realistic date for them to prove unqualified support for the security forces, the courts and the rule of law.
"We are doing nothing. The onus is on republicans to do everything. "They have to deliver support on the grounds for the PSNI, the courts and the rule of law, a complete end to paramilitarism and the removal of terrorist structures.
"Today's fiasco may have been aimed at Tony Blair, Peter Hain and the two governments, but we will not be swayed."
Former IRA prisoner Gerry McGeough, a member of the Provisionals' East Tyrone Brigade during the Troubles, was among those who criticised the vote to endorse the police. "I am not surprised by the result," he said.
"This was a classic text book case of counter-insurgency. "The British have succeeded in imposing their policy of divide and rule. A significant section of the republican movement has been recruited into the British Crown system and is being used to administer and maintain British rule in Ireland for a very long time."
Fine Gael Leader, Enda Kenny TD, welcomed the decision
"I welcome the decision of the Sinn Féin ardfheis to support the policing structures in Northern Ireland. This represents a vital move towards the establishment of democratic politics in Northern Ireland, as no sustainable devolved Government is possible without the unconditional support of every political party for policing and the rule of law," he said.
Labour Party leader Pat Rabbitte urged Sinn Féin representatives to take their places on local policing boards. He added: "This move deserves a response and I hope, in particular, that the reaction from the DUP will be positive and considered."