"The judicial board ruled to leave the Moscow City Court's verdict unchanged, and not to grant the lawyers' appeal," the court said.
Alexei Pichugin was sentenced on August 6 last year for murdering a businessman and a Siberian oil town mayor, and for the attempted murder of another businessman. He has pleaded not guilty.
Pichugin's defense said it was futile to challenge the verdict in the Russian courts.
"Now we are resting our hopes on Strasbourg [the European Court of Human Rights], where we have filed an appeal against the verdict; this appeal has been registered for consideration," defense lawyer Ksenia Kostromina said.
Pichugin's defense says Article Six of the European Convention of Human Rights, namely his "right to a fair trial", has been violated.
Once Russia's largest oil producer, Yukos collapsed after claims of tax evasion, which led to the company being broken up and sold off to meet debts. The bulk of the company's assets were bought up by government-controlled oil company Rosneft.
Former Yukos CEO Mikhail Khodorkovsky is serving an eight-year prison term for fraud and tax evasion. He has consistently protested his innocence, and called the accusations politically motivated.