Police chiefs said armed officers would be concentrating on crowded places over the festive season as well as shows, events and attractions.
Assistant Chief Constable David Hartley said the armed patrols were not aimed at frightening people but to keep them safe and to deter criminals.
Extra patrols had already started in the run up to Christmas and New Year, but anti-terror raids in Sheffield and Chesterfield on Tuesday increased their importance.
Three men were arrested in Burngreave, Meersbrook and Stocksbridge in Sheffield and a fourth in Chesterfield during a series of dawn raids.
The men, aged 22, 31, 36 and 41, are being held suspicion of being concerned in the commission, preparation or instigation of acts of terrorism.
ACC Hartley said: "Our colleagues from Counter Terrorism Policing North East arrested three men from Sheffield and one from Chesterfield on suspicion of terrorism offences and searched five addresses.
"The arrests were intelligence led and pre-planned as part of an ongoing investigation by Counter Terrorism Policing North East and MI5, which we are continuing to support.
"In light of the activity, and as planned throughout the festive period, you will see an increased visibility of both unarmed and armed patrols right across the county.
"Please be reassured that this is for your safety, to provide support and deterrence ahead of what is likely to be a busy couple of weeks."
He added: "We have a detailed understanding of all our events, shows, sporting fixtures, markets, attractions and seasonally busy places, and it’s in these places that you will see armed and unarmed staff.
"Our officers are there to keep you safe, they are not there to frighten or deter anyone from enjoying themselves over the Christmas break. Please feel free to chat to them about their role - they are normal bobbies that just happen to be armed.
"Christmas and New Year is understandably a very busy time for us but as always, we have planned our duties and resources to match this demand, so be reassured that we will be there when needed.
"Our plans over the festive season are detailed and this is about being prepared but not alarmed. My advice is to remain vigilant, but continue to go about your daily business as you usually would.
"I’d like to thank everyone for their support and patience over the last 24 hours, which has understandably caused some concern within our communities.
"We are here to keep you safe and we’ll do our very best and continue to work our absolute hardest."