Shortly after Putin spoke in a televised address on Russian state TV, explosions could be heard in the pre-dawn quiet of the Ukrainian capital of Kyiv.
Gunfire rattled near the capital's main airport, the Interfax news agency said, and sirens were heard over the city.
At least eight people have been killed and nine were wounded by the Russian shelling, an advisor to the Ukrainian Minister of Internal Affairs said on Thursday as Russia has launched massive air and ground assault on the neighbouring country.
The border guard said separately Russian military columns have crossed Ukrainian border into Chernihiv, Kharkiv and Luhansk regions.
"Putin has just launched a full-scale invasion of Ukraine. Peaceful Ukrainian cities are under strikes," Ukrainian Foreign Minister Dmytro Kuleba said on Twitter.
"This is a war of aggression. Ukraine will defend itself and will win. The world can and must stop Putin. The time to act is now."
U.S. President Joe Biden, reacting to an invasion the United States had been predicting for weeks, said his prayers were with the people of Ukraine "as they suffer an unprovoked and unjustified attack", while promising tough sanctions in response.
"I will be meeting with the leaders of the G7, and the United States and our allies and partners will be imposing severe sanctions on Russia," Biden said in a statement.
Russia has demanded an end to NATO's eastward expansion and Putin repeated his position that Ukrainian membership of the U.S.-led Atlantic military alliance was unacceptable.
He said he had authorised military action after Russia had been left with no choice but to defend itself against what he said were threats emanating from modern Ukraine, a democratic state of 44 million people.
"Russia cannot feel safe, develop, and exist with a constant threat emanating from the territory of modern Ukraine," Putin said. "All responsibility for bloodshed will be on the conscience of the ruling regime in Ukraine."
The full scope of the Russian military operation was not immediately clear but Putin said: "Our plans do not include the occupation of Ukrainian territories. We are not going to impose anything by force."
Speaking as the U.N. Security Council held an emergency meeting in New York, Putin said he had ordered Russian forces to protect the people and appealed to the Ukrainian military to lay down their arms.
Ukrainian President Volodymyr Zelenskiy said Russia had carried out missile strikes on Ukrainian infrastructure and border guards, and that explosions had been heard in many cities. An official also reported non-stop cyber attacks.
Zelenskiy said that martial law had been declared and that he had spoken by telephone to Biden. Reservists were called up on Wednesday.
Three hours after Putin gave his order, Russia's defence ministry said it had taken out military infrastructure at Ukrainian air bases and degraded its air defences, Russian media reported.
Earlier, Ukrainian media reported that military command centres in Kyiv and the city of Kharkiv in the northeast had been struck by missiles while Russian troops had landed in the southern port cities of Odessa and Mariupol.
A Reuters witness later heard three loud blasts in Mariupol.
Russian-backed separatists said they had launched an offensive on the Ukrainian-controlled town of Shchastia in the east, Russia's Interfax news agency said, and explosions also rocked the breakaway eastern Ukrainian city of Donetsk.
Hours earlier, the separatists issued a plea to Moscow for help to stop alleged Ukrainian aggression - claims the United States dismissed as Russian propaganda.
Global stocks and U.S. bond yields dived, while the dollar and gold rocketed higher after Putin's address. Brent oil surged past $100/barrel for the first time since 2014. MKTS/GLOB
'DECISIVE WAY'
Biden, who has ruled out putting U.S. troops on the ground in Ukraine, said Putin had chosen a premeditated war that would bring a catastrophic loss of life and human suffering.
"Russia alone is responsible for the death and destruction this attack will bring, and the United States and its Allies and partners will respond in a united and decisive way," he said.
NATO Secretary-General Jens Stoltenberg condemned Russia's "reckless and unprovoked attack" and said NATO allies would meet to tackle the consequences.
U.N. Secretary-General Antonio Guterres, speaking after the Security Council meeting, made a last-minute plea to Putin to stop the war "in the name of humanity'.
Ukraine closed its airspace to civilian flights citing a high risk to safety, while Europe's aviation regulator warned against the hazards to flying in bordering areas of Russia and Belarus.
Russia suspended domestic flights at airports near its border with Ukraine until March 2, its aviation agency said.
Shelling had intensified since Monday when Putin recognised two separatist regions as independent and ordered the deployment of what he called peacekeepers, a move the West called the start of an invasion.
In response to Putin's Monday announcement, Western countries and Japan imposed sanctions on Russian banks and individuals but held off their toughest measures until an invasion began.
The United States stepped up the pressure on Wednesday by imposing penalties on the Russian firm building the Nord Stream 2 gas pipeline and its corporate officers.
Germany on Tuesday froze approvals for the pipeline, which has been built but was not in operation, amid concern it could allow Moscow to weaponise energy supplies to Europe
