Putin hailed the incorporation of Crimea into Russia as a "remarkable event" before he signed the bills into law in the Kremlin on Friday.
Russia rushed the annexation of the strategic Black Sea peninsula after Sunday's hastily called referendum, in which its residents overwhelmingly backed breaking off from Ukraine and joining Russia. Ukraine and the West have rejected the vote, held two weeks after Russian troops had taken over Crimea.
The U.S. and the European Union have responded by slapping sanctions on Russia.
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