Trains began running again at 1700 GMT and service is expected to operate as normal on Tuesday, Eurostar said in a statement.
Earlier on Tuesday the cross-Channel service that links Paris, Lille and Brussels to the UK was forced to cancel 17 trains after the person was hit in Kent.
Of the 17 cancelled services, seven were from London to Paris, four from Paris to London, three from London to Brussels and three from Brussels to London.
British police were called out to the incident near Crismill Lane in Bearsted, between Ashford International and Ebbsfleet International stations at 11:40 am.
A statement from British Transport Police said: "Medics from South East Coast Ambulance Service also attended the incident, but the person was pronounced dead at the scene."
It added that the incident was being treated as "non-suspicious".
"Officers are currently working to establish the identity of the person and how they came to be on the tracks," the statement said.
The incident meant long delays from travellers on both sides of the Channel.
— Josto Maffeo (@JostoMaffeo) March 2, 2015
Stranded passengers took to social media from both sides of the channel.
(Passengers at Gare Du Nord. Photo: Veronic Irons)
We’re sorry if you’re affected by the disruptions today, for those on board please see our compensation policy here: http://t.co/Nfr0uAEkil
— Eurostar (@Eurostar) March 2, 2015
— Evening Standard (@standardnews) March 2, 2015