In a statement it cited Mann's need for medical treatment and to be with his family, adding he had "shown sufficient and credible signs of repentance and a desire to take his place in society".
Mann must leave Equatorial Guinea within 24 hours and is banned from returning to the country, it said.
Mann was arrested in March 2004 along with 61 other suspected coup plotters when their aircraft landed in Zimbabwe.
The group had planned to overthrow Teodoro Obiang Nguema Mbasogo, Equatorial Guinea's president, who has ruled the country since 1979.
Mann and Du Toit had set up Executive Outcomes, which operated from Pretoria in South Africa and helped the Angolan government to protect its oil installations from rebels during that country's civil war.
Tuesday's announcement comes as Equatorial Guinea opens its presidential election campaign on Thursday.
The vote is set for November 29 and Obiang Nguema is seeking another mandate.
The former Spanish colony is Africa's third biggest oil producer after Nigeria and Angola following the discovery of large offshore oil deposits in the early 1990s, but the benefits have yet to trickle down to the people.