The Ulster Unionist leader, Mr David Trimble, said he believed the agreement strengthened the Union between Northern Ireland and Britain and that he saw "a great opportunity to start a healing process".
It promised a more stable future for all the people of the North.
Mr Trimble said all of nationalist Ireland, "with one conspicuous exception", had accepted the principle of consent, that the constitutional status of Northern Ireland could not be changed without the consent of a majority.
In comments to the media minutes after the deal was agreed, he called on the Sinn Fein president, Mr Gerry Adams, to say "his dirty, squalid little terrorist war" was over.
There was some surprise that there were not more of Mr Trimble's senior party colleagues around as he addressed the media. Mr Jeffrey Donaldson, a member of the party's negotiating team, left the talks venue before the final plenary session. Mr Trimble said Mr Donaldson had "obligations to attend to with his young family". Mr Donaldson later denied to the Press Association that he had refused to agree to the deal, but did not comment any further.
The party deputy leader, Mr John Taylor, and Mr Ken Maginnis both stayed in Castle Buildings when Mr Trimble emerged. Mr Trimble said Mr Taylor was still attending the plenary session which was continuing.
Mr Trimble emphasised the gains unionists had made in the negotiations. "We rise from this table knowing that the Union is stronger than it was when we first sat down. We know that the fundamental act of union is there intact," he said.
He welcomed the fact that the consent principle had been accepted by the Irish Government and the SDLP, "and soon I trust we shall see it enshrined in the fundamental law of the Irish Republic". The prospect of democratic accountability was also restored in a new assembly in which the interests of all could be represented.
"We have also created a unique consultative co-operative structure which will enable all the regions of the British Isles to reflect in our interactions the many strands - social, political, cultural and economic - that exist and bound us together through the last millennium."
Asked about the delay in finalising the agreement, Mr Trimble said his party had been "gravely concerned" that in the assembly, there would be "a very real risk of those who were related to paramilitary parties getting into the administration".
He said he believed that if those parties had not demonstrated their commitment to peaceful means by decommissioning, it would be "an intolerable situation".
On this, the UUP was very much relieved by assurances given by the British Prime Minister, "that if over the course of the next six or seven months, these parties have not acted to prove their commitment to peaceful means, that he will bring forward whatever provisions are necessary, probably in the form of legislation, in order to ensure that the integrity of the democratic process is maintained".
Explaining his refusal to speak directly to Mr Gerry Adams throughout the talks, he said he would only be prepared to deal with Sinn Fein members as democratic politicians when they had established their commitment to democratic principles.
"The question now for Mr Adams is will he accept the consent principle, and also to say whether his dirty, squalid little terrorist war is over," Mr Trimble said.
Mr Trimble said the Anglo-Irish Agreement would be replaced. "A struggle that has lasted for 12 years for justice and equality for unionists in this land has succeeded." The Maryfield Secretariat of Irish civil servants would shortly close, he said.
Everybody committed to peaceful means would be able to participate in the assembly and could share in the administration of it. He said he hoped the people of Northern Ireland would endorse the agreement. "I hope that we will be able to move forwards together in a positive way. I see a great opportunity there to start a healing process here in Northern Ireland."