The paper was founded in 1979 by the first editor and then proprietor Graham Bound (who, some 40 years on, still contributes an opinion column to the paper). The first edition appeared in October of that year, with a dancing penguin motif on the cover which became its trademark for the first few years. In those early days, the PN was a duplicated publication, produced on a Roneo 750 machine that Bound described as "literally held together with rubber bands".

A one-man enterprise, PN was initially published monthly, and remained so until after the Falklands War of 1982, when the editor recruited an assistant, Robert McBride. With the editorial staff doubled and now operating in a "news-rich" environment, the paper increased its frequency of publication to fortnightly and then to weekly.

The newspaper often struggled to make enough money, but came closest to financial disaster when it was sold to Seamount Ltd in 1988, a move which was meant to secure its future. Seamount had been set up to undertake industrial fishing in the Falklands in cooperation with the government-owned Stanley Fisheries. Under this agreement, the company was required to invest in the islands in other ways, and this led Seamount to buy PN. The company's directors had experience in publishing and planned to invest in and modernise the operation. However, Seamount collapsed with major debts soon afterwards, leaving the paper's future in peril. As a temporary measure, the Falkland Islands Government, took over Seamount assets, including PN. Special legislation was then introduced establishing the Media Trust (chaired by Graham Bound for a time) to nominally own Penguin News and ensure its independence. This was modelled to some extent on the governance of the Guardian.

Editors have included Belinda Caminada, John Smith, Rory McLeod, Jim Stevens (previously a journalist on the Daily Express), Jenny Cockwell and John Fowler.

Today, the newspaper's finances are sound. The staff consists of the Managing Editor, Deputy Editor, Journalist and Office Manager, who produce a twenty-page, part colour publication printed in Stanley. The current Managing Editor is sixth generation Falkland Islander Lisa Watson. She reports directly to the Falkland Islands Media Trust.