The Fleetwood midfielder, 24, who was on Manchester United's books as a youngster, played under Shots boss Dean Holdsworth when the pair were together at non-league Newport.
Holdsworth told the club's official website: "Danny has fantastic pedigree and great quality with his left foot. He knows my style and what is expected. He shows good professionalism and I am delighted he is on board."
Rose's arrival comes with Aldershot, second-bottom in League Two, having lost their last five matches, most recently Tuesday night's 2-1 Johnstone's Paint Trophy defeat at Plymouth.
Meanwhile, striker Guy Madjo has extended his loan spell with Argyle for another two months. Madjo has scored one goal in seven appearances since linking up with the Devon club last month.
Defender Douglas Bergqvist, 19, has also penned a contract extension to remain with Aldershot until the summer of 2014.