Santana is expected to arrive in South Africa on 9 May to begin the task of coaching the 2010 World Cup hosts.
The 59-year-old replaces another Brazilian, Carlos Alberto Parreira, who announced his decision to resign on Monday to spend time with his ill wife.
Santana said he was unhappy to be leaving his Brazilian club Flamengo but was delighted with his new job.
"These things happen once in a lifetime," he said.
"Quitting here is difficult. I'm heartbroken, but I am a professional."
Flamengo vice-president Kleber Leite said: "He (Santana) told that me that he will earn in 30 months more than he has earned in the last 30 years.
"His dream is to coach a national team at a World Cup."
Santana is recognised as a journeyman professional with a good track record in Brazil.
He has little international experience, apart from brief stints with clubs in Saudi Arabia and Japan.
Parreira, 65, had been hired to prepare South Africa for the 2010 World Cup.
He put together a young and inexperienced team, which suffered a series of poor results and was eliminated in the first round of the African Cup of Nations in Ghana earlier this year.
As a result, they slumped to 71st in the Fifa rankings, but they beat Paraguay 3-0 in a friendly last month.
Parreira, whose resignation takes effect from 2 May, will continue as technical advisor, while his two assistant coaches - Jairo Leal and Pitso Mosimane - will remain part of the set-up.
Parreira recommended Santana to Safa, and says that: "He is a specialist in winning championships and has coached great Brazilian players like Romario, Bebeto and Juhnino just to name a few.
"I believe he will provide the continuity that is so crucial in preparing the team, especially with Jairo Leal and Pitso Mosimane remaining to assist," said Parreira.