It follows successful court action by Islington Council.
Protesters moved to the site in October 2011 as an extension of their presence outside St Paul's Cathedral. About 130 tents are thought to be on the site.
The Metropolitan Police confirmed they are at the site close to the City after the council obtained a possession order and injunction.
Mr Justice Hickinbottom was told the Finsbury Square camp had caused £20,000 damage to the land and the council had spent £26,000 on security.
He had refused permission for the group to appeal although they could have taken their case directly to the Court of Appeal.
A number of local businesses had complained about the camp citing anti-social behaviour by some and claims that it had attracted the homeless.
Finsbury Square become the focus for those supporting the Occupy London movement when the protest outside St Paul's was ended in February.