The 23-year-old has agreed personal terms and will officially join on 1 January 2012.
The former Manchester United reserve team captain joined Newport in 2008 from Oxford United and has score 11 goals so far this season.
Rose has represented the England C side and also spent a week on trial with Crystal Palace back in October and was reportedly an interest to the Shots manager Dean Holdsworth, whom he had formerly managed.
In a statement on the official Fleetwood Town website it read: "Town have beaten off several interested league clubs to his signature and are delighted that Danny has chosen to further his career at Highbury."
Another midfielder? Really?!