Dinamo sporting director Konstantin Sarsania said: "The transfer of Andriy Voronin can be considered accomplished.
The clubs reached an agreement and the player signed a contract for three years.
"We are delighted that such a strong player has joined Dinamo and we hope he can help solve the team's problems."
Voronin moved to Anfield in 2007 from Bayer Leverkusen, after 12 years in Germany, but scored only five goals in 27 league appearances for Liverpool.
He said: "I had options for continuing a career in Germany, and several in Russia, but eventually opted for Dinamo.
"I liked the professional approach of the leaders of the Moscow club during the negotiations, and I also liked the conversation with the head coach Andrey Kobelev.
"Our views came together. Dinamo have set high goals. I'm interested. I believe the Russian league is of a very good level."
Source: Telegraph
Source: Telegraph