Hart, who has also managed at Nottingham Forest, Barnsley, and Rushden & Diamonds, will be assisted by former Rangers' caretaker boss Mick Harford.
Rangers have acted quickly in replacing Jim Magilton and his assistant John Gorman, who both left the club by mutual consent on Wednesday.
Hart's first game in charge of Rangers will be in their game against Sheffield United at Loftus Road this coming Saturday afternoon.