Kafando, 74, has "more than three decades of extensive experience in high-level international diplomacy and politics," UN spokesman Stephane Dujarric said Friday in announcing the appointment.
A former foreign minister and UN ambassador, Kafando was president from November 2014 to December 2015 during Burkina Faso's transition to civilian rule following a military takeover and the resignation of long-serving leader Blaise Compaore.
Kafando will replace Jamal Benomar, who held the post since November 2015 and who had come under heavy criticism and calls to resign from the Bujumbura government.
Hundreds died, hundreds more have disappeared and 390,000 people fled after Nkurunziza announced plans to run for a third term, which he went on to win.
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The Security Council last month threw its weight behind a proposal by mediator Benjamin Mkapa, the former president of Tanzania, to hold a regional summit to press the government and the opposition to start negotiations.
But east African leaders appear divided on the way forward and there has been no progress towards holding talks.
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