The decision comes five years after US authorities shut down Dotcom's file-sharing website Megaupload and filed charges of conspiracy, racketeering and money laundering against the men.
Dotcom, who lives in New Zealand, has been fighting extradition since then in a case which has moved with glacial slowness at times.
And Monday's decision will not be the last, with the case likely to be appealed up to New Zealand's Supreme Court.
US prosecutors say Megaupload raked in at least 175 million US dollars (£141 million), mainly from people using it to illegally download songs, television shows and movies.
The New Zealand district court ruled in 2015 that Dotcom and the others were eligible for extradition on the charges.
High Court judge Justice Murray Gilbert found on Monday that the district court made mistakes in its ruling but that those did not alter the big picture.
Dotcom tweeted: "We won but we lost anyway."
The US argues that the site cost copyright holders, which included Hollywood's major movie studios, more than 500 million US dollars (£403 million).
Prosecutors say intercepted communications show the men talking about being "modern-day pirates" and "evil".
Dotcom argues he cannot be held responsible for others who chose to use his site for illegal purposes, and that any case against him should have been heard in civil court.
Born in Germany as Kim Schmitz, Dotcom has long enjoyed a flamboyant lifestyle. He was arrested in New Zealand in 2012 after a dramatic police raid on his mansion.
Out on bail soon after, he released a music album, started another internet file-sharing company called Mega, and launched a political party which unsuccessfully contested the nation's 2014 election.
In addition to Dotcom, who founded Megaupload and was its biggest shareholder, the US also wants to extradite former Megaupload officers Mathias Ortmann, Bram van der Kolk and Finn Batato.
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