A spokesperson from the North East Counter Terrorism Unit (NECTU) has confirmed that police are now searching five addresses.
One of the houses raided was in Shirebrook Road, Sheffield, where locals claim they heard an explosion at around 5.30am (local time).
Residents said officers then arrived at the scene and carried out a search, and the house remains under police guard.
Five addresses in Sheffield - including one in the Meersbrook area, two in Burngreave and one in the Stocksbridge area - and another in Chesterfield, are being searched by police.
Police have also sealed off the Fatima Community Centre in the Burngreave area of Sheffield.
A large number of police vehicles are parked outside the two-storey building and officers are guarding the main entrance, which is cordoned off with tape.
It appeared that the main door to building is on the floor in pieces.
A further raid in Chesterfield at Whittington Moor has led to Cavendish Junior School keeping children inside as a precaution.
One man who lives close to the raid in Brunswick Road said he was woken at 6am by three explosions in quick succession.
He said he thought one of the bangs came from the community centre but the others appeared to come from nearby flats.
The man said he looked out to see at least six men with rifles in camouflage and full body armour.
He said: "They were in full kit with the guns and everything. We're on the front line here."
He said he saw them bring out one man and put him in a police van.
The man said the building used to be the local Irish club but was taken over about 10 years ago and is now used as a mosque and a community centre.
He said: "There are people in there all hours of the day and night."
Asked if he was surprised this had happened on his doorstep, he said: "No".
Simon Fox, 22, who lives near one of the raided properties, said: 'We have seen army, police from all over, we have seen a couple of packages being removed by the bomb disposal unit.
"You just don't expect this to happen in such a small town."
A next door neighbour of the house in Shirebrook Road said he knew who lived next door and they were "all nice lads."
The man, who did not wish to be named, said: "I heard a big bang, which turned out to be the charge they used to open the door.
"I then went to my housemate and we were watching the whole thing from out the window, we saw various armed special forces and the counter terrorism unit coming in and out and then the guy came out.
"I don't know the guys from next door very well but we have had fires in the past and they have come down, they seemed like nice lads, it's a shame really.
"I am shocked."
A police spokesperson has confirmed that a loud bang heard by residents was not an explosion but a bang created when they were gaining entry.
Police confirmed all the properties are currently being searched and the men have been taken to a police station in West Yorkshire for questioning.
The arrests were intelligence led and pre-planned as part of an ongoing investigation by Counter Terrorism Policing North East.
A spokesman for the North East Counter Terrorism Policing Unit added: "The men have been taken to a police station in West Yorkshire for questioning.
"The arrests were intelligence led and pre-planned as part of an ongoing investigation.
"Three properties in Sheffield and one in Chesterfield are currently being searched in connection with these arrests.
"We recognise that local people may have concerns as a result of this activity. We would ask people to remain alert but not alarmed and we are grateful for the assistance and understanding of people locally.
"Residents will be kept as informed as possible and we are grateful for their understanding, patience and support while these enquiries continue."
South Yorkshire Police Superintendent for the Sheffield area Una Jennings said: "I understand our local communities will have concerns about this morning's police activity but I want to offer my reassurance that we will continue to serve and protect the public of South Yorkshire.
"We work very closely with our colleagues at the North East Counter Terrorism Unit and we will ensure we maintain these strong links in order to provide a high level of service and delivery to everyone in our community.
"Public safety is our utmost concern."
