This original story has been updated because the quoted source, Politiken, was misinformed about the situation. 

The Danish Ministry of Digital Affairs is only testing the possibility of migrating from MS Office to LibreOffice and is not looking to ditch Windows for Linux. 

The original Politiken article now includes the following passage:
"Clarification: In an earlier version of this article, it was stated that the Ministry of Digital Affairs would replace the Windows operating system with Linux and be free of Microsoft by the fall. This is not correct. That statement has therefore been removed. The ministry will only replace Office 365 with LibreOffice."

Below is the original story published by Linux Magazine on June 16, which includes the aforementioned inaccuracies:
Another major organization has decided to kick Microsoft Windows and Office to the curb in favor of Linux.

The Danish Ministry of Digital Affairs has decided to cut ties with Microsoft Windows and Office and adopt Linux and LibreOffice.

As first reported by Politiken, Denmark is poised to make a major change with regard to the software it uses. The migration from Windows/Office to Linux/LibreOffice will take place between June and August for half of the Ministry of Digital Affairs, and the rest of the staff will follow suit between September and November.

The move is happening because Denmark's Minister for Digital Affairs, Caroline Stage Olsen, indicates that Denmark wants to have control over its data and systems.

According to Jan Damsgaard, head of the Department of Digitalization at Copenhagen Business School, “Denmark, as the most digitised country in the world, is completely dependent on American tech companies, and that is clearly not a sustainable situation.” He continues, “I think it’s very good that the digitalisation ministry is among those to try out these open source systems."

Copenhagen (Denmark's capital) had already planned on cutting ties with Microsoft, because of concerns that political fallout could lead to the inability to send emails or communicate internally.

Copenhagen isn't the only town planning on making the shift. Aarhus (the second largest city in Denmark) also plans to make the move.

Of course, the Ministry of Digital Affairs does have a backup plan to revert to Microsoft products if the migration proves too complicated.