A Russian-born American has been named to replace Mikhail Khodorkovsky as the head of Russia's largest oil company.
Mr Kukes is one of Russia's most admired executives
Yukos said its board of directors had appointed Simon Kukes as chief executive, replacing Mr Khodorkovsky, who resigned on Monday.
Mr Kukes, 56, emigrated from the Soviet Union to the US in the 1970s but has since returned to Russia.
He was previously head of TNK, the Russian oil firm which recently agreed to merge with Britain's BP.
Mr Kukes tried to reassure investors worried over a government probe into Yukos' affairs which led last week to Mr Khodorkovsky's arrest on fraud and tax evasion charges.
"This will all be resolved, it will calm down," Mr Kukes said.
'Business as usual'
He added that there would be a smooth transition between his leadership and that of Mr Khodorkovsky, who is currently awaiting trial in a Moscow jail.
"Mr Khodorkovsky was a very strong leader, but a team was set up with clear responsibilities. With his departure, nothing will change," he said.
Many Russians believe the case against Mr Khodorkovsky, who made his fortune through controversial privatisations in the 1990s, is politically motivated.
He has funded opposition groups, breaking what analysts say was a tacit agreement to stay out of politics in return for avoiding investigation of his financial affairs.
The crackdown on Yukos and its boss has stirred fears of a wider confrontation between the Kremlin and big business.
The appointment of Mr Kukes follows a stubborn defence by Russian President Vladimir Putin of his government's role in the Yukos crisis.
He said the detention of Mr Khodorkovsky was neither evidence of authoritarianism nor a sign that Moscow was considering renationalising privatised industries.
Speaking to Italian journalists ahead of a state visit to Italy, Mr Putin said the Yukos case was about law enforcement.
"There will be no de-privatisation or revision of privatisation results," he said. "But one and all should learn the skill of living by the law and observing the law of the country."
He compared Mr Khodorkovsky's fate to that of the "score of US company bosses" arrested in the past two years.
"But nothing extraordinary happened," he told Italian daily Corriere della Sera, "and no one questioned the existence of the rule of law. For us too, it is nothing exceptional."
Even so, the investigation into the privatisations of the 1990s, and those who made money out of them, could be widening.
Russian MP Vladimir Yudin has complained to prosecutors about irregularities in the $137m sale of another oil firm, Sibneft, to Roman Abramovich.
Mr Abramovich recently sealed a deal to sell up to Yukos, and is shifting his resources overseas, a trend demonstrated by his recent purchase of the UK's Chelsea Football Club.
Yukos shares, which rose by 12% following Mr Khodorkovsky's resignation, closed flat at $12.55 on Tuesday.
He said he now planned to dedicate himself to his Open Russia Foundation - an organisation he set up to promote an open and democratic Russia.
A BBC Moscow correspondent says this suggests that Mr Khodorkovsky is preparing to bring forward his declared intention to enter the political arena.
Mr Khodorkovsky also suggested that his resignation would help disassociate Yukos from the charges of fraud and tax evasion that he faces.
In a statement, he said he "must do my utmost to lead our working team out from under the attack which has been directed against me and my partners".
Analysts welcomed the move.
"Investors saw that Mr Khodorkovsky has put a distance between himself and the company which is seen as a very good step," said Russian stock market expert Michael Sito.
Analysts also said Mr Kukes' US citizenship would make it more difficult for Russian prosecutors to take action against him.