The Russian president has long coveted a meaningful place alongside the planet's heavyweights in G7, and today he will realise that ambition as part of a trade-off for reluctantly accepting the first wave of Nato expansion on to the territory of the former Warsaw Pact.
For him, the gathering is a chance to remind the world that, though it is down - and may yet have further to fall - Russia is not out. Its economy is in ruins, and its army in tatters, but Moscow still sees itself as an influential global player, worthy of a place at the table alongside the likes of Japan, Germany and the United States.
The three-day summit, in Denver, Colorado, is also an opportunity for Mr Yeltsin to advance Russia's case for the next kick-back flowing from Nato's expansionist ambitions - membership of the World Trade Organisation and the Paris Club of creditors, a body which Moscow hopes will reinforce its efforts to recoup billions of dollars owed to the former Soviet Union.
The landscape has changed since the G7 gathered last July in Lyons, France. Mr Yeltsin had just had a heart attack, and was too sick to attend in person, sending his Prime Minister, Victor Chernomyrdin. Although the 21-month war was winding down, the blood of some 80,000 victims was still fresh on the soil of Chechnya. The Kremlin was bracing for a battle with an uncompromising Nato over its plans to move on to soil that used to be Russian stamping ground.
Since then, relations with the West have warmed. Mr Yeltsin made an almost miraculous recovery from heart surgery and double pneumonia, and decided to nail his colours to the masts of two economic reformers - Boris Nemtsov and Anatoly Chubais.
Under their influence, the president has drawn in the country's horns, by adopting a generally softer approach to foreign policy in order to concentrate on the country's domestic crisis. In the last few months alone, Russia has recognised the borders of the Ukraine, watered down a union with the dictatorially-run Belarus, and signed a peace treaty with the Chechens.
The shadow of the now wasting bear still hangs menacingly over her neighbours, especially in the Baltics. But the anti-Western mood of last year has eased. There are signs that Russia at last acknowledges that it has lost its bullying rights, and that the great power era is over.
This weekend's events - renamed "the Group of Eight" by Bill Clinton in Russia's honour - offers Mr Yeltsin the chance to indulge in a small flight of fantasy. He will have access to all but one 90-minute session of the talks, which will range across a variety of subjects. The Japanese have made clear that they intend to beard the Russian president over the Kurile Isles. And when the summit ends, the final communique will begin with the words, "we, eight industrialised democracies of the world".
The Russians are delighted by this, and seemed undaunted by the fact that it is extremely doubtful whether this description can accurately be applied to their nation, which has seen its GNP shrivel to almost half its former size in five years.
Last night, after giving a cheerful television interview, Mr Yeltsin flew out of Moscow after publicly congratulating himself on a partial victory in his effort to persuade his parliament to introduce a tax code. His arrival in Denver early today will be another sign that Russia knows that it must integrate further into the global economic system, if it is to solve its larger economic problems. And, for that reason alone, the applause will be genuinely heartfelt when the lights go up on the Boris Plus Seven Show.