Kafando was selected after several hours of negotiation, which had begun the previous day.
The 72-year-old described the appointment as "more than a honour".
"It is an awesome responsibility that falls to me, I already foresee the pitfalls and the immensity of the task," he told reporters.
Kafando previously served as the country's ambassador to the United Nations from 1998 to 2011. He was also Burkina Faso's foreign affairs minister between 1981 and 1982.
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Initially Paul Ouedraogo, the Catholic archbishop of the southern Bobo-Dioulasso diocese, appeared to be a frontrunner despite his reluctance, but the Church later announced "categorically" that he was not in the race.
"The consensus candidate is Michel Kafando," said Ignace Sandwidi, a representative of the Catholic Church, which was involved in the discussions to find a new leader.
Kafando's appointment will now have to be ratified by the Constitutional Council.
It comes ahead of a deadline imposed by the African Union, which instructed Burkina Faso to establish interim institutions and pick an interim president by today or face sanctions.
Initially Paul Ouedraogo, the Catholic archbishop of the southern Bobo-Dioulasso diocese, appeared to be a frontrunner despite his reluctance, but the Church later announced "categorically" that he was not in the race.