Internacional confirmed the news on their official website without revealing any of the terms.
Reports in Portugal say a US investment firm called Doyen Sports had purchased the striker for around R$41m (£10.8m).
Damiao became one of the hottest properties in world football by scoring 90 goals in 179 games for Internacional over the course of four seasons and helped his club to victory in the Copa Libertadores, the Recopa Sudamericana and three Gaucho state championships.
He has been capped 15 times by Brazil, scoring three goals.
He also starred at the London 2012 Olympics and ended the tournament as top scorer with six goals.
Brazil lost the gold medal match to Mexico 2-1.
The 24-year-old was often linked with a move to Europe but will instead stay in Brazil to try and earn a place in their World Cup squad.