The panels from the Marienkirche in the city of Frankfurt an der Oder were taken by the Soviet army at the end of World War II and brought to the Hermitage Museum in St.Petersburg in August 1946.
The 111 panels, which form part of the church altar that rises 20 meters (65 feet) high, were among the most sought after items for return by Germany because the church is marking its 750th anniversary next year. Both houses of the Russian parliament had passed a law providing for the panels' return in April.
Each of the panels is one square meter (10.75 square feet), used to form three large windows of the church, said Hermitage spokeswoman Larisa Aerova.
"The Hermitage offered to start the restoration process itself, but the German side preferred to do all the work," Aerova said.
On Saturday, Germany handed back to Russia seven czarist-era paintings that Nazi troops had looted during the war in a ceremony attended by culture ministers from both countries on the 61st anniversary of German troops invading Soviet territory.
Russia and Germany have accelerated exchanges of looted art under the good relationship formed between Russian President Vladimir Putin ( news - web sites) and German Chancellor Gerhard Schroeder.
Russia has proclaimed art seized from German state ownership as retribution for the damage the Soviet Union suffered in the war, which left some 27 million Soviet citizens dead.