"We have an agreement," Danish Prime Minister Anders Fogh Rasmussen told reporters after a two-day summit of hard haggling over numbers, and the future of agricultural subsidies.
He said the financial arrangements agreed at the summit would now put to the 10 applicant countries - Cyprus, Malta and eight East European nations - in Copenhagen on Monday.
Formal invitations to become members will be issued at a mid-December EU summit in Copenhagen, bringing to an end the Danish six-month presidency of the union.
Under the deal hammered out in Brussels:
"This has been a very successful summit. It represents a major step forward towards the historic decision on enlargement," said Mr Rasmussen.
Candidates shortlist
Cyprus
Czech Republic
Estonia
Hungary
Latvia
Lithuania
Malta
Poland
Slovakia
Slovenia
"Now we have an agreement that gives the [European] Commission and the presidency the necessary mandate to finalise negotiations with the 10 candidate countries."
He said he was confident the applicant countries would accept the deal on offer.
The main obstacle to an agreement was removed on Thursday, when France and Germany agreed to a compromise on their long-standing differences over the future of the Common Agricultural Policy (CAP).
Shared pain
The UK and the Netherlands, headed a group of members saying that the deal did not go far enough to limit the size of the bulging CAP budget, but appear to have lost the argument.
Mr Blair insisted on adding a line to the summit declaration saying that the agreement to cap subsidies until 2013 was "without prejudice" to a more fundamental overhaul of the system.
France, which favours the continuation of the CAP in its present form, hit back by repeating its demand for an end to the UK rebate, President Jacques Chirac describing it as "the last unreformed cost in the EU budget".
BBC correspondent Tim Franks says the deal reached involved pain for all sides, but the leaders accepted it as a price worth paying for the reunification of Western and Eastern Europe.
No date for Turkey
The leaders said they hoped Romania and Bulgaria would be ready to join the EU in 2007.
But while they praised Turkey's progress towards meeting EU membership criteria they did not set a date for the beginning of entry negotiations with Ankara.
In other decisions, the EU leaders agreed:
EU foreign policy chief Javier Solana said he would seek Turkey's approval for the text on the rapid reaction force next week.
Although Turkey is not a member of the EU, it is a member of Nato, and has been barring EU access to Nato assets.
The proposal on Kaliningrad will be put to Russian President Vladimir Putin on 11 November.