Raul de Taunay told reporters the country's proximity to South Africa, which hosts football's biggest tournament from June 11, was the major factor in the decision, which delighted Zimbabwean officials.
"Zimbabwe was chosen because of ... being close to Johannesburg," he said. "I want to congratulate Brazil for taking such a decision."
At nearly 1,500 metres above sea level, Harare is at a similar altitude to South Africa's highveld region that will host a number of World Cup games, including the final in Johannesburg.
Zimbabwe, ranked 110th in the world, were initially meant to play North Korea in a pre-World Cup friendly but the game was scrapped last month after protests over Pyongyang's role in training an army unit accused of killing thousands of people in the 1980s.
Muzembi said three companies, including a local unit of the world's second largest platinum producer Impala Platinum Holdings, had paid 70 percent of Brazil's appearance fees, with the government meeting the remainder.
Brazil will arrive on Tuesday, a day before the match and could also visit the Victoria Falls, Zimbabwe's top tourist resort, officials said.
"We are going to do our utmost best for the Samba boys so that they can have a hospitable experience that they have never experienced before," Muzembi said.
