Mr Mandelson, the Secretary of State for Northern Ireland, said the past year had brought a "quiet yet quite astonishing revolution" and there was a "growing sense of calm optimism" and normality throughout the province.
But he stressed in his Christmas message: "No longer must anyone live under threat of violence. That is why decommissioning has to happen." He added: "It is a voluntary act but one that is an essential part of the Agreement, as all the parties have now accepted."
The Ulster Unionist leader, David Trimble, has said he will resign as First Minister and pull his three colleagues out of the new power-sharing Stormont executive if the IRA does not start to hand over its guns in the next few weeks.
Mr Mandelson said Northern Ireland could look forward to a bright future as former enemies now sat in an administration that represents everyone in the province. He said that the new British/Irish institutions set up under the terms of the Good Friday Agreement also reflected the new era.
"They are common-sense organisations with the issue of consent at the centre, each designed to encourage partners to work together to solve problems, to share experiences and to find the best possible common solutions. All these are encouraging signs that the Good Friday Agreement is working but the transition must be complete, the agreement must be implemented in full."
The Secretary of State said he was conscious that Christmas was a painful time for those who had lost loved ones in the past 30 years of violence. "That pain puts a particular responsibility on all of us to make sure that the peace we are creating is unbreakable."
Mr Mandelson, who has been Secretary of State since October, said he wanted to use his role to encourage overseas investment in the province. "We have to tell the world the question mark over Northern Ireland that made people think twice about investing, about bringing new jobs here, has lifted," he said.