The Megaupload founder is wanted in the United States on charges of copyright infringement, racketeering and money laundering.
The US had opposed Kim Dotcom’s proposal to broadcast the hearing on YouTube.
He said on Twitter that the decision was “breaking new ground” and streaming would start on August 31.
Kim Dotcom’s lawyer said the move was “democracy at its finest”.
“It provides everybody in the world with a seat in the gallery of the New Zealand courtroom,” Ira Rothken told the AP, saying there would be a 20 minute delay on the live feed.
The German-born entrepreneur ran file-sharing site Megaupload.com, which once had million of users storing files and downloading movies and songs.
The FBI took control of the website and other domain names belonging to the business in January 2012. Federal prosecutors said it had cost movie studios, music labels and other copyright-holders more than $500 million in lost revenue.
In December 2015, a New Zealand court ruled that Kim Dotcom could be extradited to face charges of copyright infringement, racketeering and money laundering.
Kim Dotcom’s lawyers launched an appeal, arguing that he should not be held responsible for the actions of the site’s users, and did not get a fair hearing.
The request for livestreaming came on the first day of the appeal hearing in Auckland, which is expected to last up to eight weeks.
Another defense lawyer, Ron Mansfield, said there were “unprecedented issues of public and international interest” raised by the case and added that coverage should not be limited to traditional media.
Lawyers for the United States had said streaming could influence a potential future jury.
The High Court judge, Justice Murray Gilbert, criticized the fact the request had not been made in advance but said he wanted to hear the views of local media outlets before making a decision.
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