The Scottish champions were without a head in the dugout after Steven Gerrard left to take charge of Aston Villa last week.
Van Bronckhorst’s appointment marks a return to Ibrox, where he spent three seasons as a player, winning two Scottish Premier League titles, two Scottish Cups and one Scottish League Cup.
The 46-year-old also had spells at Arsenal and won the 2005 UEFA Champions League with Barcelona.
Van Bronckhorst, who captained Netherlands at the 2010 FIFA World Cup in South Africa, has previously managed Feyenoord in his homeland, leading them to one Eredivisie title, and Guangzhou RF in the Chinese Super League.
"I am absolutely delighted to be returning to Rangers as the club's new manager," said Van Bronckhorst, who will be presented on Monday.
"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 Ross Wilson and the board of the club, and I'm grateful for the chance to work again at this huge club.
"I cannot wait to meet the club's incredible supporters again and begin this new era for us all."
Van Bronckhorst’s first game in charge will be against Sparta Prague in the Europa League next Thursday.
