The announcement comes as Putin and US President Barack Obama are pushing rival plans on ways to defeat the Islamic State group in Syria and the role of the country's embattled leader Bashar al-Assad.
"The Federation Council unanimously supported the president's request," the Kremlin's chief of staff Sergei Ivanov said in televised remarks after the upper house approved Putin's request to deploy troops abroad.
"We are talking about Syria," he said, adding that the decision to launch air strikes was taken after the Syrian president asked Russia for military support.
Ivanov declined to give details of the operation, saying only it would have a limited timeframe, and also ruled out ground operations by Russian troops.
Putin is seeking to muscle his way back onto the world stage after months of Western isolation after Russia's seizure of Crimea from Ukraine and support for a separatist insurgency in the east of the ex-Soviet country.
Russia is later Wednesday presiding over a special UN Security Council meeting on countering terrorist threats that is bound to throw up a sharp difference of views between Moscow and Washington over the crisis in Syria.
At the United Nations on Monday, the Russian strongman proposed a broad UN-backed coalition to fight IS militants and clashed with Obama on the future of Assad.
France, meanwhile, has launched a probe into Assad's regime for alleged crimes against humanity, a judicial source said.
Paris prosecutors opened a preliminary inquiry on September 15 into alleged crimes committed by the Syrian government between 2011 and 2013, the source told AFP in Paris.
The French investigation is largely based on evidence from a former Syrian army photographer known by the codename "Caesar," who defected and fled the country in 2013, bringing with him some 55,000 graphic photographs.
The Syrian Observatory for Human Rights monitoring group said meanwhile that France's first air strike on the Islamic State group killed at least 30 jihadists, including 12 child soldiers.
President Francois Hollande said Sunday that six French warplanes hit an IS training camp near Deir Ezzor city, and that more strikes could follow in the coming weeks.
For its part, Russia argues that the West should support Assad in his fight against the jihadists, but Obama said at the United Nations on Monday that the Syrian leader must go if the Islamic State group is to be defeated.
The Pentagon says Russia has in recent weeks sent bombers, fighter jets, at least 500 troops and a slew of other military hardware to northwestern Syria in what many fear is an attempt to keep the war-torn country's president in power.
Moscow already has a powerful military detachment on a Syrian airbase in government-held territory, equipped with warplanes and tanks, and will now work more closely with neighbouring Iraq.
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- Limited timeframe -
Putin had earlier Wednesday submitted to the Federation Council a proposal to deploy "a contingent of troops" abroad, the Kremlin said in a statement, without specifying the region.
"All our partners and allies will be informed about the decision today and specific information will probably be also passed along by the military structures," said Ivanov, a former defence minister.
Senators had debated the issue behind closed doors, said Federation Council speaker Valentina Matviyenko.
Putin had also sought permission from the Federation Council to deploy military forces in Ukraine ahead of the annexation of Crimea in March 2014.
- National interests, not ambitions -
Ivanov said that by moving to launch air strikes in Syria, Russia was guided by national interests only.
"We are not talking about achieving some foreign policy goals, satisfying someone's ambitions -- what our Western partners regularly accuse us of."
On Tuesday, Russia snubbed a US-led counter-terrorism summit at the United Nations, sending a low-level diplomat to the talks.
Moscow is setting up an intelligence task force together with Iraq, Iran and Syria but US experts have so far refused to take part in its work, the Kremlin said.
Moscow's proposal has exposed differences among Washington's European allies, with some siding with Obama and others saying Moscow should have a greater role in the plan to fight IS extremists.
Washington and its allies blame Assad for the mayhem in Syria but have refused to put boots on the ground, despite the chaos after four years of intense bloodshed.