The 46-year-old becomes the 17th manager in the club’s history, replacing Steven Gerrard who left for Aston Villa a week ago.
Van Bronckhorst quickly emerged as the front runner to take over the Ibrox hotseat and held positive talks with Rangers sporting director Ross Wilson at the weekend.
It is understood the club held talks with other candidates but the 106-time Netherlands international remained the favoured option.
The announcement comes ahead of Rangers’ Premier Sports Cup semi-final clash with Hibs on Sunday.
Van Bronckhorst spent three seasons at Ibrox as a player in the late 90s to early 2000s under countryman Dick Advocaat, impressing as a technical midfielder before making an £8million move to Arsenal.
As a manager, he enjoyed notable success at Dutch giants Feyenoord. Having had two spells at Rotterdam club as a player, he led them to their first league title in 18 years, plus two KNVB Cups.
He then spent last year as manager of Chinese side Guangzhou R&F.
“I am absolutely delighted to be returning to Rangers as the club’s new manager," Van Bronckhorst said.
“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 football club.
“I cannot wait to meet the club’s incredible supporters again and begin this new era for us all.”