Brown will now take charge of Zimbabwe at the 2007 ICC World Twenty20 tournament in South Africa.
The 47-year-old Curran succeeded former West Indies all-rounder Phil Simmons in September 2005 and was in charge of Zimbabwe for 42 matches, winning nine and losing 28 while there was a tie against Ireland at the World Cup, a no result and three abandoned matches.
In a statement, ZC said Curran, whose last series ended in a 3-0 whitewash against South Africa on Sunday, had been re-assigned but did not state the former Zimbabwe all-rounder's new role.
"Zimbabwe Cricket has appointed Robin Brown as national coach, with effect from the first of September, 2007," read the statement.
"The 56-year old former Zimbabwe captain takes over from Kevin Curran, who has been re-assigned."
After his appointment, Brown said: "I am very lucky to get the job and I am excited about it. The guys are currently on a high. I hope I can continue with the re-building and get some positive results for Zimbabwe."