The episode, as related by a senior British official, captures perfectly the central achievement of this weekend's summit: after the acute strains of the Kosovo crisis, relations between Moscow and the West are back on track.
Mr Yeltsin's arrival at yesterday's meeting of the G8 (the world's seven leading industrial powers and Russia) had been awaited with much trepidation. Would he come? Would he be in a fit condition to take part? Would he create a scene?
From the moment he stepped off the Ilyushin jet at Cologne airport, the answer was clear. "We must all make up with each other after our fight," he said to waiting journalists, his step stiff, unsteady and slow, yet ebullient none the less.
The mood was evident in the vast bearhug which Mr Yeltsin gave his host, the German Chancellor Gerhard Schroder, and in his keenly awaited bilateral session with President Clinton after the G8 meeting.
If history takes its intended course, Cologne will go down as one of the group's most productive summits since they began in 1975. Mr Blair said a "bridge of understanding" had set Russia back on the path of integration with the international community.
On the economic front, in an unacknowledged reward for Russia's reluctant agreement over Kosovo, the G8 said it would push for an agreement between Moscow and the International Monetary Fund on the promised $4.5bn (pounds 2.8m) IMF loan needed to stave off a massive loan default later this year.
A deal with the IMF would clear the way for a debt rescheduling pact with the "Paris Club" of wealthy nations led by G8 members Germany, France and Italy - Moscow's biggest creditors. This could include an effective write-off of some borrowings inherited from the former Soviet Union, which, as its successor state, Russia has agreed to honour.
Henceforth, Russia will be more closely involved in the G7 talks from which it was once virtually barred. The other group members will step up assistance to emerging small businesses in Russia. There is also an informal agreement to speed Moscow's entry into the World Trade Organisation.
But a separate "partnership for the prosperity of Russia" declaration that the summit heads had planned to issue was scrapped. Apparently, Russia felt it would implicitly confirm the country's supplicant status in its dealings with the West.
The new mood may bring a revival of the stalled arms negotiations between the United States and the former superpower. In his bilateral meeting with Mr Clinton, the Russian President promised to do his best to persuade the Duma to ratify the Start-II nuclear arms reduction pact, which will limit each country's nuclear warheads to 3,000. He also promised to press for the resumption of negotiations on a Start-III treaty, which would further reduce the number of warheads, and on the amended Anti- Ballistic Missile Treaty which the US is seeking.
Finally, Moscow is normalising its relations with Nato, broken off when the bombing of Yugoslavia began on 24 March.
The question now is whether the good intentions will survive the realities of politics in Moscow. The largest party in the Duma is the anti-Western Communist party, and the anti-Nato military establishment must swallow Friday night's de facto surrender to the limits imposed by Nato on Russia's peace-keeping role in Kosovo. If there is no doubting Mr Yeltsin's belief that Russia's future lies in collaboration with the West, there are grave doubts about his health and his control of the military.
But in Cologne the optimism was almost universal. "I was struck by the smiles of everyone today," President Jacques Chirac of France said. "They were smiles of relief [at the Kosovo settlement], but also smiles of satisfaction. This was a victory for everyone, a victory for the allies, but also a victory for Russia over herself."
Russia and the West, he said, were "on the ground together, sharing the same vision, and the same objectives".
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