Three of them, aged 22, 36 and 41, were arrested by counter-terrorism officers in Sheffield while the fourth man, aged 31, was arrested in Chesterfield in an operationled by the North East Counter Terrorism Unit.
An army bomb disposal team was later called in at a house in Chesterfield in Derbyshire.
A cordon has been set up and nearby homes are being evacuated at the site in central Chesterfield, police said.
"The arrests were intelligence led and pre-planned as part of an ongoing investigation by Counter Terrorism Policing North East," a West Yorkshire Police spokesperson said.
All the four men have been detained on suspicion of being concerned in the commission, preparation or instigation of acts of terrorism under the UK's Terrorism Act 2000.
The men are being questioned at a police station in West Yorkshire while searches were being carried out on the property from where they were arrested.
Derbyshire's Assistant Chief Constable Bill McWilliam said: "We of course understand that police activity of this nature can be unsettling. However, be reassured, the arrest we wanted to make has been made.
Earlier, members of the public reported the sound of an explosion as police raided an address in Meersbrook, Sheffield.
"The public may have heard a loud bang at the time as police entered one of the properties, but it was not an explosion. They [officers] would like to reassure them that it was part of the method to gain entry to the property," the police spokesperson said.
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