Masud Shafie, a lawyer for the two brothers, told RFE/RL's Radio Farda that Arash Alaei was sentenced to six years and his brother Kamiar Alaei to three years in prison.
Kamiar and Arash Alaei have been in custody since June, and the European Union has called for their release.
Rights groups including Human Rights Watch, the International Campaign for Human Rights, and Physicians for Human Rights have condemned the arrests and legal processes as unfair and politically motivated.
The brothers are known as Iran's leading specialists in HIV/AIDS.
Reports had already emerged suggesting the Alaei brothers were convicted in a secret trial in early January.