The funeral service at Moscow's Troyekurovskoye Cemetery will come after a public ceremony at the Andrei Sakharov rights center, where Nemtsov's body is currently located.
Apart from Nemtsov's relatives and close friends, mourners include Russian Deputy Prime Minister Arkady Dvorkovich, former British Prime Minister John Major, US Ambassador to Russia John Tefft, head of the EU Delegation to Russia Vygaudas Usackas and a group of Nemtsov's supporters.
Earlier, a wreath from Russian President Vladimir Putin was reportedly delivered to the Andrei Sakharov rights center.
55-year-old Boris Nemtsov was shot dead on Friday night while walking across a bridge in central Moscow with his girlfriend, a Ukrainian model named Anna Duritskaya, who survived unscathed.
Russia's Investigative Committee has opened a criminal case into Nemtsov's murder.