Updating MPs following the naming of the two suspects in the Novichock nerve agent attack in March, the Prime Minister said the assassination attempt would "almost certainly" have been approved at a "senior level of the Russian state".
Mr Skripal and his daughter Yulia became seriously ill after coming into contact with a nerve agent believed to have been made in the former Soviet Union.
A police officer was also hospitalised. Dawn Sturgess died and her partner Charlie Rowley fell ill after coming into contact with a perfume bottle that contained the poison used in the attack.
"Based on a body of intelligence the Government has concluded that the two individuals named by the police and CPS are officers of the Russian military intelligence service, also known as the GRU," Mrs May said.
"The GRU is a highly-disciplined organisation with a well-established chain of command. So this was not a rogue operation.
"It was almost certainly also approved outside the GRU at a senior level of the Russian state."
With Russian law forbidding the extradition of its own nationals, Mrs May said a European Arrest Warrant had been sought for the arrest of Alexander Petrov and Ruslan Boshirov - believed to be aliases.
“Should either of these individuals ever travel outside Russia, we will take every step to extradite them to face justice here”, she said.
“We will deploy the full range of tools across our security apparatus in order to deter the threat from the GRU.”
The Prime Minister told the Commons that CCTV evidence "clearly" places the two Russians in the vicinity of the Skripals' house shortly before the attack on them.
"This hard evidence has enabled the independent Crown Prosecution Service to conclude they have a sufficient basis on which to bring charges".
Mrs May said around 250 detectives had trawled through 11,000 hours of CCTV footage to identify the attackers and had taken more than 1,400 statements.
"Working around the clock, they have carried out painstaking and methodical work to ascertain exactly which individuals were responsible and the methods they used to carry out the attack," she told MPs.
When asked to account for what happened, Mrs May said Russia had replied with "obfuscation and lies", including claims that she had invented Novichok.
The Prime Minister added: "Their attempts to hide the truth by pushing out a deluge of disinformation simply reinforces their culpability."