Russia has announced all military bases in Crimea are under its control and Ukrainian troops have left the region.
Russian Defence Minister Sergei Shoigu added the country's president, Vladimir Putin, would hand over the military vessels and airplanes of Ukrainian forces that have changed sides and joined Moscow.
The region voted overwhelmingly to join Russia in a hastily-arranged referendum earlier this month.
Vladimir Putin signs a bill confirming the annexation of Crimea US President Barack Obama has urged Russia to pull its forces back from Ukraine's border amid the biggest crisis in relations between the West and Russia since the end of the Cold War.
"You've seen a range of troops massing along that border under the guise of military exercises. But these are not what Russia would normally be doing," he told US television network CBS.
Russia was accused of invading Crimea in the aftermath of the removal of President Viktor Yanukovych, but Mr Putin called the soldiers who took over Ukrainian bases there "self-defence forces".
US President Barack Obama However, on Friday the Russian leader said the action in Crimea had showed the new capacities of the Russian army.
"The recent events in Crimea were a serious test," he said at a televised military ceremony.
"They demonstrated the new capacities of our armed forces in terms of quality and the high moral spirit of the personnel."
Ukraine shares a vast border with Russia It is the first time Mr Putin has confirmed the direct involvement of the Russian army in the seizure.
He went on to thank the "commanders and servicemen of the Black Sea Fleet and other units deployed in Crimea for their restraint and personal courage".
On Friday Mr Yanukovych said every region of Ukraine should hold a vote to decide whether to break away like Crimea.
Armed men, believed to be Russian, sit in an armoured vehicle in Crimea He said he would not recognise a presidential election planned for May 25 and called instead for nationwide referendums.
"As president who is with you in thought and soul, I ask every single sensible citizen of Ukraine not to let yourselves be used by the imposters.
"Demand a referendum on determining the status of every region in Ukraine," he added in a statement quoted by Russia's ITAR-TASS news agency.
Mr Yanukovych faced months of mass protests over his decision to spurn a European Union trade deal in favour of closer ties with Moscow.
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