Several services on the route had to be scrapped following the incident, which began on Friday evening and ended when a suspect was arrested around 12 hours later.
A British Transport Police (BTP) spokesman confirmed eyewitness reports that the protester was waving an English flag.
The incident began on the day the UK was originally due to leave the EU, and followed a day of Brexit protests in Westminster.
A Eurostar statement said: “We have suspended all services to and from London St Pancras this morning, due to a trespasser on the tracks outside of St Pancras.
“We are not allowed to run any services in and out of London St Pancras at the moment and strongly recommend you not travel this morning and please cancel your journey or exchange ticket free of charge for a different date.
“We apologise for any inconvenience caused.”
The operator said a reduced timetable had been implemented, with customers being told they could exchange their ticket or apply for a refund.
It added: “The trespasser on the tracks outside of St Pancras has been apprehended and our services will be able to start to run in the area again soon. We would still recommend you not travel this morning and please cancel your journey or exchange ticket.”
A BTP statement said: “A 44-year-old man has this morning been arrested for trespass and obstruction of the railway, having spent the night on the roof of St Pancras Railway Station.”
The previous evening, BTP confirmed a man was “in a precarious position” at the London terminal.