A Golden Arrows official confirmed the news to KickOff.com on Monday, as Middendorp takes charge of the team with immediate affect.
He will have to wait for his work permit to come through before he can sit on the bench, but with Abafana Bes'thende's next match only on April 6 against SuperSport United, it should be through in time.
Former Montenegrin national team coach Filipovic joined Golden Arrows at the start of the season, taking over from Manqoba Mngqithi who had jumped ship to KwaZulu-Natal rivals AmaZulu.
After initial success, where Golden Arrows won five of their first eight fixtures and sat in the top three, the club's season has imploded.
They have won just two of their previous 18 matches in all competitions, and none of their last nine in the League. They also exited the Telkom Knockout and Nedbank Cup in the first rounds.
The results were too much for Golden Arrows boss Mato Madlala and she has moved swiftly to put the recently available Middendorp in charge.
The German was relieved of his duties at Maritzburg United on March 11 after a run of just one win in 10 had left The Team of Choice on the brink of a relegation scrap.
Middendorp, who has also coached Kaizer Chiefs, has been tasked with leading Golden Arrows back into the top eight. They currently trail eighth-placed Free State Stars by four points with five games remaining in the season.