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The Hoegh Osaka was deliberately run aground in the Solent shortly after leaving Southampton port with a cargo worth £60m on 3 January.
She spent four days stranded on the shallow Bramble Bank before freeing herself and being secured in deeper water between East Cowes on the Isle of Wight and Lee-on-the-Solent on the mainland.
The 51,000-tonne vessel was towed to Southampton port on Thursday and salvors are to hand over responsibility of the ship to the Norwegian owners Hoegh Autoliners.
It is thought the total value of the cargo could be up to £60m.
While the ship is docked in Southampton, salvors will work to make the decks safe so the owners can take back control of the vessel.
It is thought that much of the cargo is underwater but many of the cars remained securely in place while the ship was listing at 52 degrees.
The salvage company Svitzer is based in the Netherlands and has worked on operations all over the world. Salvage master Bram Sperling has worked on more than 90 missions.
Transport Secretary Patrick McLoughlin said: "I congratulate all those who have worked tirelessly day and night to bring this ship back to port.
"I would like to pay particular tribute to Hugh Shaw who oversaw the operation, with the help of the Maritime and Coastguard Agency, salvage operators, and the pilots and tugs of the port of Southampton.
"They battled exceptionally difficult weather conditions with extraordinary dedication and courage. A full investigation into how the incident occurred is ongoing."
The Marine Accident Investigation Branch is to investigate the incident fully once the ship has been secured by the salvage team.