Until now only larger forces, including the Met in London, Greater Manchester and Thames Valley Police have had counter-terrorist specialist firearms officers.
But sources have told the Daily Star Sunday all 43 forces in England and Wales will get access to them.
While smaller constabularies such as Dorset and Devon and Cornwall may share armed units, most will have their own. Officers will be ready to deploy around the clock.
Last week members of the new CT teams were training in London, where they were using their skills to abseil from helicopters and storm buildings in mock attacks.
Police will also be trained in hostage rescue operations and to carry out sniper attacks against armed terrorists.
One source said: “Up until now the Met has led the way in counter-terrorist operations but every police force must be able to respond to a terrorist incident.
“MI5 believes that jihadists are now based in every major town and city in the UK. They are hiding in plain sight. No one knows where they will strike next.
“Police can no longer wait for the SAS or the Met’s specialist counterterrorist teams to get them out of trouble.”
The CT teams will be equipped with SIG 516 semi-automatic carbines and Glock 9mm sidearms. And some forces plan to copy the Met and have armed officers capable of racing to the scene of any potential incident on board specially adapted BMW motorcycles.