Oleg Pylev, assumed leader of the Orekhovo-Medvedkovo criminal group, was sentenced to life imprisonment in a high-security facility, while the actual killer, Alexei Sherstobitov, was given 23 years. Kvantrishvili headed the Sportsmen Social Protection Foundation.
The remaining two participants in the crime were given 11 and 13 years.
The prosecution and victims' representatives said they would not appeal the verdict.
"The only thing to be mentioned is that certain episodes have not been solved in full, but we hope in the long run all those guilty will be punished," a representative of the victims said.
Lawyers for the convicted men said they would appeal the verdict in the Russian Supreme Court.