Moscow: Days after holding referendums, Russian President Vladimir Putin has signed laws to formally take over the four regions Donetsk, Luhansk, Zaporizhzhia and Kherson into the "Russian Federation."

"Russian President Vladimir Putin has signed four federal constitutional laws on the entry of the Donetsk and Luhansk People's Republics, Zaporizhzhia and Kherson regions into the Russian Federation," said the lower house of Russian parliament Wednesday citing government documents.

"He also signed the relevant laws on ratification," it added, reported Al Jazeera.

This comes after last week's developments where both houses of the Russian parliament ratified treaties making Donetsk, Luhansk, Kherson and Zaporizhia regions part of Russia.

Russia's annexation has sparked wide criticism from around the world. The United States announced that it will impose a "swift and severe cost" on Russia.

Meanwhile, US Secretary of State Antony Blinken said that the "United States unequivocally rejects Russia's fraudulent attempt to change Ukraine's internationally recognized borders."

"We will continue the United States' powerful, coordinated efforts to hold Russia to account, cut Russia's military off from global commerce and severely limit its ability to sustain its aggression and project power," he added.

After Putin's formal announcement of the annexation of the said four regions, western leaders condemned it, termed it "illegal" and vowed that they will "never recognize" these areas.

Earlier, Putin during the formal announcement of the annexation said that the millions of ordinary citizens, whose culture has been "destroyed", carried the "love for their historical homeland in their hearts" and in the heat of the battle, "heroically" came to the referendum and made their choice to be with Russia.