Dotcom said his legal team are confident the Supreme Court will hear the appeal given there are such significant legal issues at stake.
The group lost their case in the North Shore District Court in 2015 and has now lost appeals to the High Court and the Court of Appeal.
In its ruling on Thursday, the Court of Appeal argued that the U.S. case was warranted, as it relied on "available extradition pathways" propped up by "sufficient evidence".
The Court of Appeal has ruled Mr Dotcom, plus co-defendants, Mathias Ortmann, Bram van der Kolk and Finn Batato are eligible to be extradited for their participation in alleged criminal copyright infringement, racketeering and money laundering.
The website was an early example of cloud computing, allowing users to upload large files onto a server so others could easily download them without clogging up their email systems. "We think that ultimately Kim Dotcom will prevail", Ira Rothken told the Reuters news agency.
Dotcom can take his appeal to the Supreme Court, New Zealand's final avenue of appeal, but will need compelling new evidence that he was facing a miscarriage of justice.
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The German national, who is accused of industrial-scale online piracy, had asked the court to overturn two previous rulings that he and his three co-accused be sent to the USA to face charges.
He said the precedent set is concerning, and has ramifications in New Zealand outside of his case.
However, the four accused could be extradited on the fraud charges, the judge said in his 2017 ruling, as they are crimes in New Zealand.
Mr Dotcom estimates he has spent 165 days in court and spent $40 million in legal fees on the case. Dotcom has vowed to fight the decision, saying "it has the value of toilet paper".
A Court of Appeal panel decided that Mr Dotcom could argue for further discovery from the government in relation to his case.