The 46-year-old former Light Blues player joins the Ibrox club subject to receipt of a work permit and will become the 17th permanent manager of the Scottish champions.
Van Bronckhorst told the club’s official website: “I am absolutely delighted to be returning to Rangers as the club’s new manager. I feel so lucky to be going to work with a squad which is in a great position on all fronts and largely has that experience of being winners.
“I look forward to carrying on and enhancing the work that has been done already alongside (sporting director) Ross Wilson and the board of the club, and I’m grateful for the chance to work again at this huge football club.”
The Dutchman takes over from Steven Gerrard, who left to join Aston Villa last week.
Rangers chairman Douglas Park said: “I am delighted to welcome Giovanni as our manager to begin a new era and build further on what has already been achieved at the club.
“The team is in a good position on the park and, as a board, we will support both Giovanni and Ross Wilson to continue to make Rangers a success.
“I wish Giovanni all the very best in his role and look forward to working closely alongside him.”