London on Sunday of potential delays after flooding forced the cancellation all Saturday trains.
The first Eurostar train left London St Pancras International shortly after 8:00 am (0800 GMT).
Engineers had brought water in two tunnels in Kent in southern England under control meaning that at least one tunnel was useable, it said.
But Eurostar cautioned that «there will be some speed restrictions in place in the morning which may lead to delays and stations are expected to be very busy».
The company operates services from London to Paris, Brussels and Amsterdam.
It announced late Saturday that all scheduled trains would run on Sunday after an estimated over 30,000 people were impacted by the last-minute cancellations.
Travellers were left stranded on mainland Europe while those at St Pancras scrambled to find hotel rooms or make alternative travel arrangements.
Some tourists said their New Year holiday plans had been «ruined».
A spokesman for HS1, which runs the route between London and the Channel Tunnel, said flooding was being resolved and «the HS1 line will be operational in the morning».
«We understand how frustrating this has been for passengers and apologise for the inconvenience caused at such an important time of the year.»
The company has not revealed what initially caused the flooding which began Friday night when water filled tunnels near Ebbsfleet International in Kent, blocking the high-speed rail line.
The spokesman said the cause of the flooding will be investigated, but added that there was no evidence to suggest it was caused by a burst pipe feeding the tunnel's fire safety system as had previously been suggested by a water company.