Zimbabwean intelligence reports seen by Reuters suggest Mr. Mugabe's exit was in the planning for more than a year.
The ministers had the mission to meet with President Robert Mugabe and the commanders of the Armed Forces who are controlling that country, and will present their reports to the troika.
The Gaborone meeting was attended by Angola, South Africa, Tanzania and Zambia.
Across the country, Zimbabweans were enjoying freedom they haven't had in years.
"As much as a large number of Zimbabweans are celebrating the military takeover right now, I don't believe it will necessarily change anything within the state of the country and its politics", said Meli Ncube a Zimbabwean living in South Africa. Emmerson Mnangagwa, a former security chief and life-long Mugabe confidant known as "The Crocodile" who was axed as Vice-President earlier this month, is the key player.More news: Faculty have rejected employer offer, college strike continues
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The pair managed to escape on the evening of the coup and make it to Mr. Mugabe's compound, where they remain under effective house arrest, one political source said.
Maimane said Mugabe must step down immediately and Zimbabwe should go to the polls to elect a new government. She said the better its economy, the better it was for countries in the region because of economic opportunities.
Professor Loren Landau, Director of the Wits African Centre for Migration & Society said: "Any uncertainty about the political situation in Zimbabwe will mean people will need to come to South Africa for economic and possibly physical protection".
He said the South Africa was "eating its own poison" because it was through South African intervention that Zimbabwean elections were rigged in both 2002 and 2008.
The Troika ministerial meeting is being chaired by South Africa in its capacity as SADC acting chair, says a press note from the Ministry of Foreign Affairs that reached Angop on Thursday.