The 90,465-tonne LT Cortesia was en route to the Suez Canal when it ran aground on the Varne Bank, nine miles (14km) south of Dover harbour.It was refloated on the evening tide and is now anchored off Deal with the Coastguard tug Anglian Monarch in attendance.
The Maritime and Coastguard Agency (MCA) said three commercial tugboats took an hour to pull LT Cortesia off a sandbank and towed it to an anchorage in an area called The Downs, three miles off the coast of Deal.
"I'm pleased to say that the removal of the vessel has been a success" - MCA spokesman
"Surveyors from the MCA and investigators from the Marine Accident Investigation branch will go on board once it is anchored and carry out their investigations."
The ship is expected to stay at its anchorage for up to 24 hours while the the teams work out how the vessel, which was carrying more than 42,700 tonnes of cargo, ran aground.
The MCA said they only had "one shot" at moving the ship at high tide because the tide would drop over the next few days.
The 90,465-tonne German-registered vessel had 27 people on board and ran into difficulties on the Varne Bank towards the middle of the Channel.
The MCA said none of the crew was injured and there have been no pollution leaks.
MCA spokeswoman Rosie Tapping said the container ship was registered as carrying hazardous cargo, but the exact nature of the materials on board was unknown.
She said: "It has got 4,148 containers on board, above and below deck. It is carrying a mix of cargo. As yet we don't know what it is exactly, but it would not all be hazardous. It might just be one container."
She said all vessels entering the Dover Strait are obliged to report to the Dover Coastguard if they are carrying any hazardous materials, even a single container. She added: "'Hazardous' could mean a wide range of different things -it could mean perfume."
A Dover coastguard said it was a mystery why the container ship suddenly ran aground.
He said: "We haven't a clue why it ran aground. The vessel had come down normally, made an alteration to its route and then went aground. The weather has been fine and its traffic pattern was OK until the last minute when it went aground."
While the container ship was aground the Coastguard emergency towing vessel, Anglian Monarch, was on scene to help evaluate any external damage to the vessel and assess the options for salvage of the vessel.
The Dover Coastguard and the Anglian Monarch warned any approaching vessels of the potential navigation hazard posed by the LT Cortesia while she was aground.(Thanks to the BBC, ITV and the Independent for their WEB sites for news).