EU leaders yesterday opened wide the enlargement process and set in train a new treaty-changing Inter-Governmental Conference process to help prepare the EU institutionally.
Six new accession states will open negotiation on membership in March.
In Romania, the poorest of the six new EU hopefuls, President Emil Constantinescu welcomed the Helsinki announcement - but acknowledged the work ahead.
"It is a great day for Romania and for Europe. Ten years after the end of communism, the ideals for which Romanians have made sacrifices and their legitimate hope of becoming a member of the European democratic family have been granted," he said.
But Russia urged the EU to reconsider inviting Latvia to start entry talks, making fresh allegations the Baltic state discriminated against its large Russian-speaking minority.
The decision of the summit to bring six more states into accession talks was an "historical step to a united Europe", the Commissioner for Enlargement, Mr Gunther Verheugen, said yesterday.
"The Iron Curtain has most definitely been removed and a period of uncertainty ends."
The Minister for Foreign Affairs, Mr Andrews, described it as "a very important day".
Bowing to pressure from the six who were left behind last year - Latvia, Lithuania, Slovakia, Bulgaria, Romania and Malta - the leaders have acknowledged the demotivating effect of being deprived of a target date for accession talks.
But Mr Verheugen was quick to deny that the EU had made a mistake which it was now putting right.
"The reason was not to correct a mistake but a change in the political situation," he insisted. They were learning the lessons of Kosovo, he said.
"Enlargement is the best way to achieve peace."
Leaders also agreed to set the end of 2002 as the deadline for the EU's internal preparations, notably the ratification of institutional changes agreed in the context of next year's IGC.
That means, realistically, that the earliest new accession is unlikely to be able to happen before mid to late 2004 because each one also requires the unanimous ratification of member-states.
Leaders also insisted that the notion of two waves of admissions to the Union was no longer on - each applicant would be treated as an equal and judged on its individual merits.
The President of the Commission, Mr Romano Prodi, strongly urged leaders to give the IGC an open-ended remit to allow some of his radical ideas about treaty reform to be introduced to its discussions next year. A source close to Mr Prodi said of today's likely conclusions to the debate that he was still "optimistic that doors will not be shut" on more radical ideas.
But a core of leaders, not least the Irish, but also, among others, the British and the Germans, are very keen not to get involved in a complicated ratification process for any treaty changes agreed in Nice next December. The Government has been advised that if the changes are limited to the small range of institutional matters left over from Amsterdam a referendum would not be required.
Mr Prodi may have to play a longer game. Some observers were speculating that although the IGC would complete its work on the "leftovers" of Amsterdam it could also prepare the way for yet another IGC two years later to deal with the more radical agenda - another IGC is required by the Amsterdam Treaty before the EU accepts more than four new members.
The three unresolved Amsterdam issues are the reduction to one per member-state of the number of commissioners, the reweighting of votes in favour of the larger member-states in the Council of Ministers, and an extension of qualified majority voting.
Also to be dealt with are any treaty-changing requirements arising from both the development of institutions dealing with the EU's new military dimension and next year's debate on a charter of rights for the EU's citizens.
In the case of the former, the Irish have made clear they do not regard treaty changes as legally necessary.
And although an elaborate broad-based structure is being established to work on the charter, its scope and legal standing are still uncertain.