The First Minister spoke out about the “appalling and horrific” developments as Boris Johnson led a crisis meeting of senior ministers and officials to consider how to respond to the military action.
But he insisted that Mr Putin had “chosen a path of bloodshed and destruction” with his attack, pledging that the UK and and its allies would respond “decisively”.
Explosions could be heard in the Ukrainian capital of Kyiv shortly after a televised address from the Russian leader, while explosions were also reported in the cities of Odesa and Kharkiv.
Mr Putin insisted in his address, early on Thursday morning, that his action was in response to threats from Ukraine, claiming that Russia was not seeking to occupy Ukraine and insisting the responsibility for bloodshed lay with the Ukrainian “regime”.
He also warned other countries that any attempt to interfere with the Russian action would lead to “consequences they have never seen”.
Ms Sturgeon tweeted that the overnight developments in Ukraine “however anticipated – are appalling and horrific”.
She stated: “The Kremlin must face the severest consequences for this unprovoked aggression.
“And the world must stand in solidarity with the people of Ukraine.”
On Wednesday Ms Sturgeon met the acting consul general of Ukraine, Yevhen Mankovskyi, and Linda Allison, the chairwoman of the Scottish branch of the Association of Ukrainians in Great Britain.
In the wake of those talks she urged the UK to impose tougher sanctions against Russia, saying while there had been “some very tough rhetoric from Boris Johnson” this now needed to be “matched by action”.
Ms Sturgeon also made clear she was “appalled” at former Scottish first minister and now Alba Party leader Alex Salmond’s continued involvement with Russia Today – the Kremlin-backed TV channel on which he has a television talk show.
Labour leader Sir Keir Starmer said: “Vladimir Putin’s attack on Ukraine is unprovoked and unjustifiable. His actions will have horrendous and tragic consequences that will echo throughout the world and throughout history.
“All those who believe in the triumph of democracy over dictatorship, good over evil, freedom over the jackboot of tyranny must now support the Ukrainian people. They have been cast onto the front line of a war, simply for existing.
“There can be no space for equivocation when faced with the evil that Putin has unleashed. His actions pose a grave threat to the international order on which we all depend.
“There will be dark days ahead. But Putin will learn the same lesson as Europe’s tyrants of the last century: that the resolve of the world is harder than he imagines and the desire for liberty burns stronger than ever. The light will prevail.
“I know people in this country will be feeling worried and uncertain. I know that Ukrainians and Russians here in the UK will be worrying for friends and family back home. Our hearts are with them today.
“We must now match our rhetoric with action. We must urgently reinforce our Nato allies. The hardest possible sanctions must be taken against all those linked to Putin. The influence of Russian money must be extricated from the UK. And those who have for too long turned a blind eye to Russia’s actions must reckon with their own consciences.”
Boris Johnson said the Russian president has “chosen a path of bloodshed and destruction”, and is expected to announce further sanctions.
The meeting of the Cobra emergency committee follows a call between Mr Johnson and Ukraine President Volodymyr Zelensky during the night as Russia launched its assault.
The Prime Minister – whose initial package of sanctions was criticised by senior Tories and opposition figures – has promised to respond “decisively” to the Russian onslaught.
“I am appalled by the horrific events in Ukraine and I have spoken to President Zelensky to discuss next steps,” he said.
“President Putin has chosen a path of bloodshed and destruction by launching this unprovoked attack on Ukraine.
“The UK and our allies will respond decisively.”
A Downing Street spokesman said Mr Johnson assured Mr Zelensky the West will “not stand by as President Putin waged his campaign against the Ukrainian people”.
“The Prime Minister said he hoped Ukraine could resist, and that Ukraine and its people were in the thoughts of everyone in the United Kingdom people during this dark time,” the spokesman said.
Foreign Secretary Liz Truss said she condemns the “appalling, unprovoked attack” on Ukraine.
“I strongly condemn the appalling, unprovoked attack President Putin has launched on the people of Ukraine,” she tweeted.
“We stand with Ukraine and we will work with our international partners to respond to this terrible act of (aggression).”
US President Joe Biden said his Ukrainian counterpart Volodymyr Zelenskyy had “reached out” to him following the attack by Russian forces and asked for world leaders to “speak out clearly” against Vladimir Putin’s actions.
“I briefed him on the steps we are taking to rally international condemnation, including tonight at the UN Security Council,” Mr Putin wrote on Twitter.
“He asked me to call on the leaders of the world to speak out clearly against President Putin’s flagrant aggression, and to stand with the people of Ukraine.”
He added: “Tomorrow, 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.
“We will continue to provide support and assistance to Ukraine and the Ukrainian people.”
US Secretary of State Antony Blinken has said it is possible Russian forces commence an invasion of Ukraine before the night is over.
He told NBC News: “Russia has positioned its forces at the final point of readiness across Ukraine’s borders to the north, to the east, to the south. Everything seems to be in place for Russia to engage in a major aggression against Ukraine.
“I can’t put a date or an exact time on it, but everything is in place for Russia to move forward.”
Mr Blinken added there was “still an opportunity to avert a major aggression”, but “if Russia continues to escalate, so will we”.
The UK’s ambassador to the UN, Dame Barbara Woodward, has said it is a “grave day for Ukraine and for the principles of the United Nations”.
Speaking at an emergency meeting of the UN Security Council, she said: “As we sat in this chamber urging Russia to step back, President Putin announced special military operations on Ukrainian territory.
“This is unprovoked and unjustified. This is a grave day for Ukraine and for the principles of the United Nations.
“We and our partners have been clear that there will be consequences for Russia’s actions. We fully support the United States’ call for a UN Security Council resolution. This Council must do all it can to stop war and uphold the (UN) Charter”.
Ursula von der Leyen, President of the European Commission, said: “Later today, we will present a package of massive and targeted sanctions to European leaders for approval.
“With this package, we will target strategic sectors of the Russian economy by blocking their access to technologies and markets that are key for Russia.
“We will weaken Russia’s economic base and its capacity to modernise. In addition, we will freeze Russian assets in the European Union and stop the access of Russian banks to European financial markets.”
Speaking in Brussels, she added: “Like with the first package of sanctions, we are closely aligned with our partners and allies, the United States, the United Kingdom, Canada, but also, for example, Japan and Australia.
“These sanctions are designed to take a heavy toll on the Kremlin’s interests and their ability to finance war.”
Ireland’s Foreign Affairs Minister Simon Coveney has branded the Russian invasion of Ukraine as a “murderous act of aggression”.
Mr Coveney said a “strong response” was needed from the international community.
“Russia has launched a full-scale invasion of Ukraine. God help them,” he tweeted.
“Rocket attacks & explosions across the country. Make no mistake: this is a shocking murderous act of aggression against a sovereign peaceful state. EU and world needs to respond strongly.”