On Tuesday, the first train left Paris at 0810 local time (0710 GMT), and the first departure from St Pancras, in London, was at 0740 GMT.
By late morning, four Eurostar trains had departed from St Pancras, three from Paris and two from Brussels. Each had a capacity of 750 passengers.
Initially, Eurostar prevented customers with on-the-day tickets from boarding while it cleared its backlog, but they were later allowed on board.
Eurostar said it hoped to have carried 26,000 passengers in total by the end of Tuesday.
Passengers with tickets for travel between 19 and 24 December have been told they can go to a terminal on Wednesday or Thursday and Eurostar "will do its best to allocate a seat on the next available train".
But chief executive Richard Brown said services would not return to normal until "after Christmas".
Some passengers were relieved to get on a train, but others were still angry with the company.
Stephanie Budd, 34, from Wallington, Surrey, finally arrived at St Pancras after taking her four children to Disneyland Paris, and ending up spending three nights in Brussels.
She said: "The lack of information has been awful. Since Friday we have not known when we would be able to get home.
"It just was not explained that this would take so long. I'm so angry."
Out of service
The problems began on Friday, when five Eurostar trains broke down in the tunnel after condensation affected electrical systems.
Another train, which had been laid on to try to clear the backlog, suffered the same fate as it left the tunnel in Kent on Saturday night.
Ian Nunn, Eurostar: "We are getting people through and into trains"
The company said snow shields used to protect the trains' electrics had worked for the past 15 years, but a recent cold snap in France had been "unprecedented".
Eurostar trains were taken out of service while it tried to rectify the problem, causing a massive backlog of stranded passengers on both sides of the Channel.
The company tested modifications to trains on Monday, and said it was confident there would be no problems.
The problems with Eurostar had a knock-on effect for Eurotunnel train services carrying cars and lorries through the tunnel.
It closed its car shuttle service to new passengers on Monday after saying its terminal in Folkestone, Kent, had reached "saturation" point.
A backlog of 7,000 vehicles built up but the process of starting to clear those started on Tuesday.
Day trip bookings for travel on Tuesday and Wednesday have been cancelled.
Eurotunnel said anyone without a reservation or with a day trip ticket should contact it before setting off.
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