Under the agreement, which has been approved by the government in Nicosia, Turkey will not be obliged to recognise Cyprus before Ankara commences EU membership talks. However such a step will have to take place before Turkey actually joins the EU.
The deal is a diplomatic success for Britain, which holds presidency of the EU and is a strong supporter of Turkish accession, because it paves the way for formal membership negotiations to begin next month.
Last week the UK reached agreement with France, one of the EU's main sceptics over Turkish membership, on the terms on which talks could start.
Yesterday's deal brings Cyprus on board behind a formal EU declaration. That leaves only Austria fighting to toughen the EU's negotiating stance towards Ankara.
With the Austrian government now isolated, it is likely that EU membership talks with Turkey will begin as scheduled in Luxembourg on 3 October. Negotiations are expected to last for at least a decade.
Cyprus has been split into a Greek Cypriot-controlled south and a Turkish-occupied north since Turkey invaded in 1974, after a coup by supporters of union with Greece.
Though the government in Nicosia had wanted a timetable for recognition from Turkey, it eventually backed down, content with a clear EU statement that Cyprus's status will, eventually, have to be recognised by Ankara.
The latest row over recognition of Cyprus began in July, when Turkey acceded to EU demands to extend its customs union deal with the bloc to all new member states, including the Cypriots.
However, Ankara has thus far failed to open its ports to Cypriot vessels, despite the accord. The latest agreement creates no deadline for Turkish ports to be opened to Cypriot vessels but makes it clear that "non-discriminatory implementation" of the customs union will be seen as an important element in the EU membership negotiations.
EU diplomats still have to finalise a negotiation framework for those talks before they can begin. Austria is expected to press for the possibility that Turkey should be offered a "privileged partnership" with the EU rather than membership.
But the issues addressed in the text agreed last night, such as recognition of Cyprus, will not be reopened in that document, and Austria has few allies in its bid to spell out a "privileged partnership" option in the mandate.
The stalemate in the German elections also gave Turkey's prospects a significant boost because of the lack of a clear majority for Angela Merkel's Christian Democrats. Ms Merkel opposes Turkish accession and could have changed the position of the German government.
Last night's accord follows four unsuccessful attempts this month to agree on the wording of the statement.