Yanukovych was approved Friday by the Ukrainian parliament for the post of prime minister.
Yanukovych, who had previously served as prime minister under former president Leonid Kuchma, suffered a humiliating defeat to Western-leaning President Viktor Yushchenko in the re-run of the presidential elections two years ago following street protests against election fraud dubbed the "orange revolution."
The pro-Kremlin leader's nomination finally received Yushchenko's backing Thursday after four months of political turmoil.
Fradkov said wished Yanukovych success on his new post and said he hoped cooperation between the two countries' governments "would aim at developing and strengthening Russian-Ukrainian partnership, implementation of important prospective projects in many spheres... on the principles of mutual benefit and market economy."
Yanukovych has strong support from the Russian-speaking eastern part of Ukraine, and is widely expected to seek closer economic ties with Russia.