According to Eurostar's official Twitter page, the line lost overhead electrical power near Ashford, south east England, after lightning struck a transformer.
It initially said that four trains - two from Paris, one from London, and another from Brussels - were heading back to their points of departure.
But in a later update, the service said London-bound trains would continue to their destination. However, the train out of London returned to its departure point.
All trains finally arrived at London's St Pancras terminal by 01.40 am (0140 GMT), according to Eurostar.
"Customers are being offered taxis and hotels where necessary, but we are hoping to have everything back to normal shortly," said a spokesman.
There were no reports of any injuries, and no trains had been stuck in the tunnel.
Kent Fire and Rescue said they attended a "number of incidents" following a storm in the Folkestone and Dover areas, including an electrical substation at the Dollands Moore Freight Depot, in Folkestone.
Eurostar's website said trains were back running normally by Friday morning.