Just over six months later, Putin became Russia's second postcommunist president following Yeltsin's surprise retirement.
At the time, the former KGB colonel turned president was widely expected to dutifully carry out the policies crafted by Yeltsin's close circle of Kremlin kingmakers.
But seven years into his presidency, it is clear that Putin has proved them wrong.
Yevgeny Volk, who heads the Moscow office of the Heritage Foundation think tank, says Putin has rolled back many of the democratic reforms introduced by his patron.
"Yeltsin carried out a radical breakthrough. Of course, he remained to a large extent a man of his era, with many contradictions," Volk says.
"But he was sincere in his aspiration to freedom and his rejection of totalitarian regimes. Putin, considering his former activities, his background, could not have appreciated Yeltsin's rule, with its rights for mass media, for oligarchs, for civil organizations."
Putin has cultivated an increasingly anti-Yeltsin image.
In contrast to Yeltsin's boisterous, sometimes vodka-induced appearances, Putin appears sober, athletic, and self-controlled.
Where Yeltsin could be spontaneous, even impulsive, Putin seems calculating. (Read Yeltsin's obituary) While Yeltsin reduced the army and ensured independence for former Soviet states, Putin has boosted military spending and has sought to extend Moscow's control in the post-Soviet space. At home, Putin has dismantled the federalism championed by his predecessor by bolstering central control.
The two leaders, however, share similarities, including a readiness to use force. Yeltsin crushed opposition to his reforms in 1993 by sending in tanks to attack the parliament, where his opponents were gathered. Both leaders oversaw brutal military campaigns against separatists in Chechnya.
Nonetheless, some policy watchers have said choosing Putin as his heir was Yeltsin's biggest mistake.
Vladimir Lysenko, a deputy minister for national and regional policy under Yeltsin, shares this view.
"I think that the saddest pages of our history and the history of Boris Nikolayevich [Yeltsin] is when he, together with Boris Berezovsky, chose the successor who would lead our state after Yeltsin. Boris Nikolayevich, of course, made a colossal mistake by bringing the current head of state to power," Lysenko says.
Private Criticism Of Putin
Yeltsin has only rarely openly criticized Putin -- in 2000, when Putin reinstated the old Soviet anthem, and in 2004, when Putin scrapped the popular election of regional governors.
Georgy Satarov, a senior Yeltsin aide between 1994 and 1996, says Yeltsin was much more critical in private.
"He understood what was happening, we discussed it -- I mean the rollback of federalism. He understood all this and assessed it negatively," Satarov says.
"He was upset to an even greater extent by Beslan and the changes that started taking place after Beslan, such as Putin's abolition of the gubernatorial elections, etc. He understood all this and assessed it negatively, I can say this with certainty."
Yeltsin largely shrank from public view following his 1999 retirement. By the time the Kremlin announced his death on April 23, Yeltsin already seemed to belong to a past era.
Yeltsin, who died from heart failure, is being mourned with less pomp than might be expected for post-Soviet Russia's first president.
President Vladimir Putin's statement came some four hours after the announcement of Yeltsin's death.
Political analyst Volk says this is no accident.
"A clear effort can be seen to prevent Yeltsin's funeral from turning into some kind of political event that could be used by opposition forces, for the organization of events," Volk says. "There are obviously some fears that those who promote freedom and democracy in Russia could pick up Yeltsin's banner."
Yeltsin will be buried in Moscow's Novodevichy cemetery on April 25, only two days after his death -- significantly faster than by Russian tradition. Currently his body is lying in state.
Highlights Of Yeltsin's Life
BORIS YELTSIN: student, engineer, husband, father, professional volleyball player, Communist Party official. A timeline of the multifaceted life of Russia's first president.