Mr Yeltsin knows he will be seen as having buckled under the pressure of a narrow clique of oligarchs who exploited the privatisation of state assets to build vast fortunes - and subsequently used them to pressure the Kremlin to defend their interests. But the events of the last 36 hours may also mark a larger watershed in the rule of Mr Yeltsin, a seven year helter-skelter ride in which he has veered across the political spectrum, from autocrat to rough-hewn democrat.
The snowy-haired man who in 1991 stood on a tank outside the White House, flourishing his democratic credentials in the face of drunken Communist coup plotters, also launched war in Chechnya, surrounded himself with hardliners, and used tanks to bombard a recalcitrant parliament. Exhausted by hard-living, heart trouble and the task of trying to pilot the country through the post-Soviet chaos, this same man may now have concluded that it is time to ease his way out.
"It looks like the President is starting to withdraw from office step by step, handing over power to the heir," said his arch-enemy Mikhail Gorbachev. For once, the former Soviet leader's views did not sound purely like sour grapes. Mr Yeltsin loves power, and is a master at centralising it on the Kremlin. He is also incorrigibly unpredictable, whether in his ludicrous exploits - drunkenly conducting an orchestra in Berlin, pinching a secretary - or in politics. He proved that yet again last Sunday, sacking his government at the height of a fiscal crisis, adding political chaos and limbo to the economic maelstrom. What he does today, he can - and often does - undo tomorrow.
Witness the case of Anatoly Chubais, his financial trouble-shooter whom he has sacked three times. In addition, the zealous Sergei Kiriyenko was almost certainly fired because he was construed as threat to the oligarchs' empires - which are rooted in energy, banking and the media. Several feared his government would allow their banks to collapse, unable to pay vast foreign debts.
But, having bankrolled Mr Yeltsin's election campaign in 1996, they appear to have called in the favour by demanding a compliant prime minister.
Yet signs are beginning to surface which suggest Mr Yeltsin may now have accepted his rule is winding down. The well-connected Ekho Moskvi radio station quoted sources saying Viktor Chernomyrdin had insisted, as a condition of his return to office, that he has the right to appoint the head of the "power ministries" - the Interior Ministry, the Federal Security Services and the Ministry of Defence. No one understands the importance of retaining control over the security forces better than Mr Yeltsin. If the story is true, then it amounts to a significant reduction of his powers.
In his speech to the nation yesterday, the President clearly anointed Mr Chernomyrdin as his preferred successor in the election of 2000. His departure cannot come too soon for his growing army of critics, whose ranks embrace the majority of Russians, almost all the lower house of parliament, and plenty of enraged international investors, who view Mr Chernomyrdin's appointment as the kiss of death to Russia's efforts to make the transition to a healthy market economy.
They point to the evidence that he is no longer up to the job. Although he appeared to recover well from the quintuple coronary bypass in late 1996, questions have repeatedly arisen over his mental state. This theme has a bleak familiarity for Mr Yeltsin, who these days appears far older than his 67 years. He has long been prone to bouts of depression and withdrawal, and has openly admitted to "dark thoughts". A best-selling account by his former bodyguard Alexander Korzhakov claimed that Mr Yeltsin had twice tried to commit suicide by leaping in the Moscow river and locking himself in a steam bath.
There is certainly little doubt that he had a nervous break-down when he was banished by Mr Gorbachev to the Soviet construction ministry in 1987. Although he has retained a gift for springing political surprises, the number of embarrassments has grown.
During a trip to Sweden late last year, he appeared unsure of where he was, and seemed to think Germany and Japan possessed nuclear arsenals. Last Friday, he appeared to refer to the US attacks on Sudan and Afghanistan as an "act of terrorism". And only three days before the government announced its decision to devalue the rouble last Monday, Mr Yeltsin was publicly declaring that devaluation "won't happen ... It is not a question of what I think, of my own fantasies, of what I do or do not want to see. It is all calculated."
True, this may have been a last-ditch attempt to build confidence in the beleaguered currency; but it is as likely that he was simply out of touch. After all, he had been on holiday for five weeks despite a rapidly worsening political crisis.
How long he will stay in the Kremlin now depends on several factors. He is mindful of his place in history, which will at least give him credit for holding the first democratic transfer of power in Russia for a thousand years. He will want to be sure that Mr Chernomyrdin stands a strong chance of succeeding him, and will defend the interests of the ruling elite that has evolved during the Yeltsin years. This could conceivably mean striking a deal with the Communist-nationalist opposition which includes rewriting the constitution to allow the president to be appointed not by popular vote, but by parliament.
And much rests on the advice of the so-called Kremlin "Family", dominated by his daughter and image-maker, Tatyana, and his chief of staff, Valentin Yumashev. As Russians look on with bewilderment as the Kremlin staggers from one disaster to another, there are plenty who hope that the old man's aides will now gently tap him on the shoulder, and point to the door.