Pro-Russian soldiers have been in de facto control of Crimea since last month
Russian President Vladimir Putin has signed a decree recognising Crimea "as a sovereign and independent state", presidential sources say.
"This decree enters into force on the day on which it is signed," they add.
The move follows Sunday's referendum in Crimea in which officials said 97% of voters backed breaking away from Ukraine and joining Russia.
The EU and US earlier imposed sanctions on a number of officials from Russia and Ukraine over the vote.
The Russian presidential decree was issued "considering the expression of the will of the people of Crimea at the general Crimean referendum, which was held on 16 March 2014," the text of the decree said.
Earlier, the Crimean parliament formally declared independence from Ukraine and applied to join the Russian Federation.
The referendum was called by the pro-Russian authorities in Crimea after the ousting of Ukraine's pro-Moscow president Viktor Yanukovych, who had sparked months of street protests by rejecting a planned EU trade deal in favour of closer ties with Moscow.
Pro-Russian forces have been in control of Crimea since late February. Moscow says the troops are pro-Russian self-defence forces and not under its direct control.
The EU, US and authorities in Kiev have rejected the referendum as illegal.
The EU and US earlier published separate lists of sanctions against both Russian and Ukrainian government officials and lawmakers, including the acting prime minister of Crimea, Sergei Aksyonov, and Crimea's speaker of parliament, Vladimir Konstantinov.
The US list included Dmitry Rogozin, a Russian deputy prime minister, Valentina Matviyenko, head of the upper house of the Russian parliament and the ousted Ukrainian leader, Viktor Yanukovych.
US President Barack Obama said in a press conference that Washington stood "ready to impose further sanctions" depending on whether Russia escalated or de-escalated the situation in Ukraine.
But he also stressed there was still a path to solve the crisis diplomatically.
EU foreign policy chief Catherine Ashton said those singled out for travel and asset bans were responsible for threatening Ukraine's territorial integrity and independence.
But there was still time to avoid "a negative spiral" in the situation, she added, urging Russia to withdraw its forces from Crimea.
Russian Deputy Foreign Minister Sergei Ryabkov said the US measures reflected a desire to impose its own unilateral, unbalanced approach.
Ukraine's acting President Oleksander Turchinov said Kiev was ready for negotiations with Russia, but it would never accept the annexation of Crimea.
In a televised address, Mr Turchinov said that any actions inciting mass disorder would be viewed as "abetting the military aggressor and a crime against the state".
The Kiev authorities earlier said they had recalled their ambassador to Moscow for consultation.