The announcement by the Russian Foreign Minister, Andrei Kozyrev, to Nato ambassadors is a landmark in post-Cold War Europe, but Russia attached conditions to its approval, and the news is likely to be greeted with concern in Eastern Europe, whose path into Nato is far from sure.
Mr Kozyrev signed Nato's Partnership for Peace (PFP) deal, which is aimed at creating stronger links between the alliance and its former Cold War adversaries.
He also agreed another document, a Summary of Conclusions that creates a broader dialogue between Russia and Nato. Moscow had insisted that this was essential because of its unique status and had postponed signature from April.
In a 45-minute restricted briefing to ambassadors, Mr Kozyrev said Russia had 'no fundamental objections to Nato enlargement,' alliance sources said.
He would be visiting Poland, the first candidate for membership, very shortly to discuss the issue. He also said that Russia had accepted an invitation for a summit in September between President Bill Clinton and Russia's President, Boris Yeltsin.
The signal on new members comes at the end of a tough negotiating period in which it has been made clear by Moscow that any changes in the alliance must be discussed. Moscow began to accept the idea last year, when Mr Yeltsin signed a memorandum of understanding with Poland's President, Lech Walesa, saying Russia would not block Polish entry. Subsequently Russia has exacted a price for its agreement, slowed down the pace of change and gained a place at Nato's table.
Yesterday Mr Kozyrev said there were three conditions for Russia's approval of new membership.
First, Russia would one day like to join Nato, and the door had to be kept open.
Secondly, the pace had to be slow; there was no need to rush.
Thirdly, when new members joined, a new strategic relationship would have to be created between Russia and Nato, giving Moscow a more solid role in the chief institution of European collective defence. Elements of that strategic relationship are already clear from the Summary of Conclusions. It establishes 'the development of a far-reaching, co-operative Nato-Russia relationship, both inside and outside Partnership for Peace'. It recognises Russia as 'a major European, international and nuclear power'. And it establishes information-sharing, political consultations and security co-operation. But Nato's Deputy-Secretary General, Sergio Balanzino, said: 'There will be no vetoes or droit d'egard over each others' affairs.'
Poland, Hungary, the Czech Republic and possibly Slovakia are likely to be in the first intake into Nato. The alliance will start moves to create a 'fast track' for them next year through PFP, Nato sources say, though membership is some way off.
They are also going to be in the first group of new states into the European Union and its defence offshoot, the Western European Union, by the end of the century.
Nato and WEU membership are likely to come before full EU membership.
Yesterday's agreement has been greeted with considerable bitterness by some of the Eastern European countries. They see it as creating a new European security condominium above their heads.
The prospect of Nato membership for Central Europe is of little comfort to the Baltic republics and the Ukraine, none of which is likely to gain entry to Nato soon, if ever.
And these are precisely the countries on which Russia, through its stress on the 'near abroad', is increasingly focussing its foreign-policy attentions.
Even some alliance analysts accept that the result of the deal with Russia has to some extent been to draw a new line across Europe, something which Nato has resisted. But they point out that Ukraine will be safer when it borders a Nato country, and that it should benefit from an easing in East-West military tension. The Baltic republics are also being encouraged to build stronger bilateral links with Scandinavian countries.