MOL Ship Management said the salvage team was able to board the Felicity Ace on Friday and a tow line attached the salvage tug Bear. The car carrier is to be towed to a safe area off the Azores.
The ship manager said that smoke was no longer visible leaving the vessel.
Two tugs ALP Guard and Dian Kingdom, and a large salvage craft with additional firefighting capability VB Hispanic are escorting the car carrier.
The blaze on board the vessel started on 16 February and the 22 crew were safely evacuated.
German media quoted an internal email from Volkswagen that the MOL vessel was carrying 3,965 vehicles of the Volkswagen, Porsche, Audi, and Lamborghini brands. Some 1,100 of the vehicles were from Porsche. The cargo has been estimated to be worth in the region of $400m.
