Formal letters were served on Wednesday by Sheffield City Council officers, supported by the police, instructing the occupants to leave the site by 12pm today, Friday, August 6.
This comes after a number of residents have complained about the use of the park by those who are camped there, and concerns about the state it may be left in once they have moved on.
John Teasdale, who lives opposite the park, said: “This happened last year and the council just put big boulders by the skate park, but did nothing to stop people getting onto the field.
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"I live opposite the park, and I counted 50 caravans before I lost count. They have completely taken over the park so nobody else can use it.
"They all arrived last Sunday, and the park wsas full in about three hours. It was a week before anything was done about it.
"It is in a right state. There’s toilet paper and litter everywhere. It will cost a lot to clean up.”
Councillors Mike Levery, Alan Hooper and Ann Whitaker said they had asked officers to visit the site to determine whether they will comply.
If not, they said, an eviction notice will be sought from the High Court.
The councillors said in a joint statement: “The council has to follow the legal process, and the travellers know that. We want a quick resolution to this as much as local residents do.
“Once they have left, we will review the options for securing the site against future visits whilst maintaining easy access for local residents.”
MP for Penistone and Stocksbridge Miriam Cates added: “A public park used by families and children is a completely inappropriate place for this type of encampment, and residents have told me of the impact it is having on the local area.
“I will be updating constituents who have emailed me on the situation as soon as I have more information from the Council.”
As of 2pm, August 6, a resident said that there were around 10 caravans left on the field, and that the travellers seemed to be complying with the notice to move on.