The company said it was "very sorry" for the disruption and offered passengers with tickets for cancelled trains the chance to exchange them for another day.
Some of those passengers who were affected on Monday said there were upset with Eurostar for failing to provide updates.
The disruption threatens to hit Paris Fashion Week with leading industry figures taking to microblogging website Twitter to highlight their travel difficulties.
High-speed trains in and out of Lille also experienced serious delays on Monday afternoon and evening after heavy snow brought down power lines, the national SNCF railway service said.
"The great majority" of train services in the north, including the Eurostar to London, were back on track before midnight transport minister Thierry Mariani told the French news agency later.
Eurostar said all delayed trains heading for London had arrived. It added that Tuesday's first scheduled service to Paris - at 5:40 GMT - was due to run on time but that the next four services would be cancelled.
A normal service is expected to resume after lunchtime Tuesday.
Heavy snowfalls also cut powerlines in northern France on Monday leaving some 140,000 homes without electricity. Around Douai, Lens, Hazebrouck, and Bethune, the electricity company EDF said it was struggling to repair powerlines.
The Lille-Lesquin airport was also closed for a few hours in the middle of the day because of heavy snow.