This means that a terrorist attack is "highly likely", although Mrs May stressed that there is no information to suggest an attack is imminent.
She said: "The Joint Terrorism Analysis Centre (JTAC) is responsible for setting the national threat level. That informs the decisions of security professionals across the public and private sectors about the appropriate level of security in place across the United Kingdom.
"JTAC's judgements about that threat level are made on the basis of the very latest intelligence and are independent of ministers.
"JTAC has today raised the threat level to the UK from international terrorism from SUBSTANTIAL to SEVERE. That means that a terrorist attack is highly likely, but there is no intelligence to suggest that an attack is imminent."
It is understood that there is no intelligence relating to any specific threat to the forthcoming Nato summit.
The decision comes against a backdrop of increasing concern about hundreds of aspiring British jihadis travelling to Iraq and Syria to learn terrorist "tradecraft", and the murder of American journalist James Foley by an apparently English killer.
Sir Bernard Hogan-Howe, the UK's most senior police officer, said Scotland Yard is prepared for an influx in case a swathe of homegrown extremists decide to return at the same time.
In a statement released today, Mrs May said: "The increase in the threat level is related to developments in Syria and Iraq where terrorist groups are planning attacks against the West. Some of those plots are likely to involve foreign fighters who have travelled there from the UK and Europe to take part in those conflicts.
"The first and most important duty of government is the protection of the British people. We have already taken steps to improve our powers and increase our capabilities for dealing with the developing terrorist threats we face. That process will continue and the British public should be in no doubt that we will take the strongest possible action to protect our national security.
"We face a real and serious threat in the UK from international terrorism. I would urge the public to remain vigilant and to report any suspicious activity to the police."
There are five levels of threat used by the JTAC. These are:
:: Critical - an attack is expected imminently.
:: Severe - an attack is highly likely.
:: Substantial - an attack is a strong possibility.
:: Moderate - an attack is possible but not likely.
:: Low - an attack is unlikely.
National Policing Lead for Counter-Terrorism Assistant Commissioner Mark Rowley said: "We need communities and families to bring to our attention anyone they perceive may be vulnerable, a danger or escalating towards terrorism. Anyone with information is urged to contact the Anti-Terrorist Hotline on 0800 789 321.
"From this afternoon we will begin to increase our levels of visible patrols and implement other security and protection measures. We will also build on existing community relations to provide reassurance and seek their support and assistance in keeping the UK safe."