Police said the individuals will now only be able to attend hospitals for a medical reason, under the terms of community protection notices handed to each of them.
West Mercia Police also issued the men with fixed-penalty notice fines for breaching Covid-19 lockdown regulations.
A criminal investigation was launched after videos appeared online while were filmed inside the Queen Elizabeth Hospital in Birmingham and the Alexandra Hospital in Redditch. Hospitals in Worcester and Kidderminster also featured, before the footage was deleted.
On January 12, the force said it had arrested two men, aged 31 and 34, from Bromsgrove, a 34-year-old from Droitwich and another male, 27, from Kidderminster, on suspicion of causing a public nuisance.
The men were questioned in relation to filming incidents in the hospitals, as well as Bromsgrove town centre and a park in the town, all said to have happened between December 31, 2020, and January 9 this year.
The force said it had decided to hand the men community protection notices which are designed to curb anti-social behaviour, after their actions “disrupted” hospitals.
The videos were filmed at the peak of the strain on the NHS, and just days after the arrests the number of UK daily deaths within 28 days of a positive Covid test hit a record high of 1,820, on January 20.
Inspector Lee Page, from West Mercia Police, said: “During the first few days of 2021 the NHS was close to being overwhelmed at the peak of the second wave of the Covid-19 pandemic.
“West Mercia Police received numerous complaints from concerned members of the public and medical staff about the actions of a group of individuals who were live-streaming from hospital sites in Worcestershire, protesting that the pandemic was a hoax.
“The men were not wearing face coverings or socially distancing and some of them were challenging hospital staff, accusing them of spreading fake news and claiming there was no national emergency and no pandemic.
“The behaviour of these people disrupted the running of the hospitals, tied up valuable resources and caused alarm and distress to patients and staff, some of whom made official complaints to police.
“As a result of their activities, West Mercia Police issued written warnings to all four people under Part 4 of the Anti-Social Behaviour Crime and Policing Act 2014.
“These warnings directed them not to enter any hospital in England unless for medical reasons, as well as prohibiting a number of other anti-social activities.
“Officers also reported all those involved for fixed-penalty notices due to breaches of the health protection regulations.
“I hope this case highlights that although everyone is entitled to freedom of speech and freedom of expression, when this negatively impacts on the health of NHS staff, patients and the wider community, we will not hesitate to take enforcement action to keep the public safe.”