Senior Ulster Unionists who support the devolution-decommissioning deal have echoed Mr David Trimble's call for Sinn Fein to "jump" next and deliver on decommissioning.
The UUP security spokesman, Mr Ken Maginnis, said the ball was now in Sinn Fein's court.
"We have placed the onus fairly and squarely before the eyes of the national and international community on Sinn Fein. They can no longer complain that somehow they haven't an opportunity to move from the mode of violence to the mode of democracy," Mr Maginnis said after the meeting, while hecklers shouted abuse at him in front of the Waterfront Hall.
One of the UUP's chief negotiators, Mr Dermott Nesbitt, told BBC Northern Ireland: "There are no preconditions (for Sinn Fein's entry), but obligations to be fulfilled. We are in the process of fulfilling the obligation of bringing about an inclusive government. It is now Sinn Fein's obligation to deliver on decommissioning."
Another of the UUP's negotiating team, Mr Michael McGimpsey, said he was delighted with the result. "Almost 60 per cent of the UUC have backed the party leader. Common sense has prevailed."
Mr David Ervine, leader of the Progressive Unionist Party, welcomed the vote. "I'm quite happy with the result. It's where we've wanted to be for a long time."
He felt Mr Trimble would not have secured 58 per cent approval for his proposals at the UUC meeting had he not made provision for another meeting in February.
Mr Gary McMichael of the Ulster Democratic Party also welcomed the vote, saying, "The only way to test the viability of the Good Friday agreement and the commitment of republicans to conform to the democratic process is by implementing the agreement."
Ms Monica McWilliams, one of the two Northern Ireland Women's Coalition Assembly members, welcomed the outcome and praised the leadership of Mr Trimble.
The Church of Ireland Primate, Dr Robin Eames, said: "All those involved in violence in the past should now begin the process of decommissioning. I appeal to the loyalist paramilitaries to take the lead in this regard as an act of faith in the future."
The Catholic Archbishop of Armagh, Dr Sean Brady, said: "We must always take account of people who are hurt by developments and reassure them that we are all trying to work together for a better future, for a more secure future.
"In that context, I would call on paramilitaries to begin the process of decommissioning arms, to begin disposing of their arms. In that way they too can make an important contribution to building peace and help to calm fears on all sides. They can play their part now and the opportunity is there."