Driver Jonathan Froudakis de Souza, 20, and conductor Walace Aparecido de Souza Silva, 21,  were sentenced for robbery, extortion and rape.
They abducted the American woman after she boarded the bus in the Copacabana area of Rio in March.
She was raped in front of her boyfriend, a French citizen.
Another gang member was given 21 years and a 14-year-old boy is yet to be tried.
The incident raised security concerns ahead of next year's football World Cup in Brazil and the 2016 Olympics, which the city will host.
Judge Guilherme Schilling Pollo Duarte in Rio de Janeiro said the gang had been operating in the area for months, targeting mainly foreign tourists.
The woman was "humiliated, suffering brutally at the hands of her kidnappers, in an act that caused repulsion and indignation", said Judge Pollo Duarte.
The American woman and her boyfriend had boarded the minibus late on 30 March.
The vehicle was going to Lapa, a popular nightlife spot in the old city centre.
A few minutes later, the gang robbed six other passengers who were on the minibus and forced them to get off.
But they ordered the American woman, who had been living in Rio, and her boyfriend to stay.
He was handcuffed and beaten and had his nose broken.
The driver, the conductor and another gang member took turns to rape her while the minibus was driven around the city.
"It is difficult to believe that all such acts were perpetrated by human beings," said Judge Pollo Duarte.
The couple were dumped in the nearby city of Itaborai after being forced to use their credit cards to buy goods and withdraw money from cash machines.
The gang member sentenced to 21 years was Carlos Armando Costa dos Santos, 21.
The 14-year-old cannot be named for legal reasons. He has been accused of rape and robbery.
After the incident hit the headlines in late March, other women recognised the gang members and said they had been the victims of similar attacks.
Two men in Brazil have been sentenced to 49 years in jail each for kidnapping and repeatedly raping an American woman on a minibus in Rio de Janeiro.