Known as Vivaldi and available on desktop computers from Tuesday, the browser's initial launch covers the Windows, Mac and Linux platforms.
"A mobile phone and a tablet version are in the pipeline. We are working on it, but they won't be out until they're ready," said von Tetzchner, who owns 90 percent of the company's shares and has paid for the development.
"At some point it will need to fund it self and to reach that point we will need a few million users. I have no doubt that we will reach that number quite easily," he added.
With features like personalised notes, bookmarks with small screen shots and speed dials with options for multiple groups and folders, Vivaldi hopes to attract high-volume users.
Despite tough competition from the likes of Google's Chrome, Microsoft's Internet Explorer, Apple's Safari, Mozilla Corp's Firefox and Opera Software's browser, von Tetzchner believes there is still room for more.
"We welcome everyone, but this is first of all a browser for people who expect and need more," he said. "There is without a doubt a demand for this type of browser even though I don't expect it to take more than a few percent of the total market."
Vivaldi has signed a few affiliation deals ahead of the launch and is in talks with several potential partners for functionalities like search and online shopping.
"We have made several deals and have started a dialogue with others. But because some of these are potential competitors, we've wanted to go live with the browser first."
Named after the 18th century composer Antonio Vivaldi, the name carries an inescapable reference to von Tetzchner's previous role as co-founder and long-time head of browser and mobile phone technology firm Opera Software.
He left the company in 2011 and later formed Vivaldi.net, a social media platform which he said at the time would target computer geeks wary of aggressive advertising and government surveillance.