Cooley, 45, is currently head coach at CA's Centre of Excellence in Brisbane, and since 2006 has been the country's bowling coach, as well as its assistant coach for the last two years.
But he will not be applying for the head coach role full-time, with former New Zealand coach Steve Rixon and former Australian Test batsman Justin Langer reportedly in the running for the job.
'Troy has advised that he will not be an applicant for the head coach role, given his significant and important duties at the Centre of Excellence,' said Brown.
'This appointment will therefore allow the Australian squad continuity as they attempt to cement their number one one-day ranking and attempt to climb the ICC Test rankings.'
Nielsen, 43, who held the coach job for four years, stepped down last week after declining to re-apply for the expanded role of head coach -- a new post recommended by the Argus Review of Australian cricket.
The seven-month review was ordered by the Australian cricket board after the Test team's humiliating 3-1 Ashes series defeat to England this year.
Cooley said he was excited by the challenge.
'I feel excited and comfortable coming into this 'caretakers role' knowing that Michael Clarke, Shane Watson and Tim Nielsen have been planning this South African campaign for a while now,' he said.
'My immediate task will be to come up to speed with their plans and work with the players and support team to ensure the preparation is spot-on for a successful tour.
'My working knowledge of the Australian team and our opposition will no doubt be an asset in the short term as we look to build on the successful tour of Sri Lanka,' he added.
As acting coach, Cooley will also be an acting national selector.