Pichugin, 44, is already serving a 20-year sentence for two killings and an attempted murder.
"The defendant's guilt has been substantiated by criminal case materials and witness testimony," the court said in the verdict, adding that it had been mitigated because Pichugin had underage children.
The prosecution had requested a life sentence.
Pichugin was charged with the attempted murder of businessman Andrei Rybin, and the murder of entrepreneur Valentina Korneyeva and the mayor of the Siberian oil town of Neftyugansk, Yury Petukhov.
The Prosecutor General's Office brought the charges against Pichugin last July.
The other five defendants in the case, who have admitted their guilt on some of the charges, including the attempted murder of businessman Rybin and the murder of Korneyeva, were sentenced to 7.5 to 19 years in prison, the terms to be served in high-security penal colonies.
Rybin said he was satisfied with the verdict in general, although Pichugin and the other defendants were only "a tool" in other people's hands.
"The organizers of those crimes - [Leonid] Nevzlin and [Mikhail] Khodorkovsky - have not been punished for the blood they shed," Rybin said.
Khodorkovsky, founder of what was once the leading independent oil company in Russia, is serving an eight-year prison term on fraud and tax evasion charges. Nevzlin, a principal Yukos shareholder, fled the investigation and is now living in Israel. Rybin, a former Yukos executive, has accused them of ordering the killings of people who threatened the company or them personally.
The Prosecutor General's Office said it was pleased with the verdict.
"The verdict is lawful and fair," said prosecutor Kamil Kashayev. "Human life is the greatest treasure, and the 24-year prison term is an adequate punishment."
The lawyers acting for Pichugin, who argued for his acquittal, plan to appeal the verdict with the Supreme Court.
"The verdict is based on evidence given by those who perpetrated the murders and attempted murders, but Pichugin is not even acquainted with the people behind bars with him."
A law enforcement source said a new investigation has been launched against Pichugin without elaborating further.
