While today's ruling paves the way for extradition, it is subject to a judicial review.
The Supreme Court also found that the men were not eligible for extradition on the conspiracy to commit money laundering charge, but were on another 12 charges.
Since their arrests in 2012, Dotcom, Matias Ortmann, Bram van de Kolk and Finn Batato have been fighting extradition to the United States.
The authorities there say they profited from encouraging people to breach copyright by uploading files like music and movies from their MegaUpload website.
When a district court gave the go-ahead for extradition in 2015, the group challenged that with a judicial review.
The High Court and Court of Appeal dismissed the review but the Supreme Court now says it must go ahead.
The grounds for that review include procedural unfairness, breach of natural justice, errors of fact and unreasonableness.
The Supreme Court found that the Court of Appeal erred in concluding that the judicial review proceedings were an abuse of process.
It says instead the court should have looked at whether the grounds for the review had been considered by the lower courts.
The court has asked the parties to file brief submissions on the issues that remain outstanding in the judicial review proceedings and for their view on which court these issues should be resolved in.
A final decision as to whether the men are eligible for surrender will be made once the judicial appeals are resolved.
