The deal, which has been in the works for more than 18 months, appears to have been struck in response to Moscow's demands for the return of Vadim Krasikov, who is serving a life sentence in Germany for the assassination in a Berlin park.
He is now back in Russia.
The Turkish presidency said a total of 24 people held in prisons in seven countries were exchanged in Ankara.
The detainees were from the United States, Germany, Poland, Slovenia, Norway, Russia and Belarus, the statement said.
The statement added that 10 people, including two minors, were transferred to Russia, 13 to Germany and three to the United States.
