Triano was made the interim head coach Dec. 3 when the Raptors fired Sam Mitchell. Triano was signed Monday to a three-year contract but financial terms weren't released.
Toronto was 25-40 under Triano but won nine of its final 13 games. The team was 33-49 for the season, finishing fourth in the NBA's five-team Atlantic Division.
"Despite some difficult circumstances this past season, Jay Triano never stopped coaching, teaching and leading this team, which resulted in a very strong finish," said Raptors General Manager Bryan Colangelo. "After undertaking a thorough evaluation process, it is clear that Jay is the right coach to guide this team in the future."
Triano was the head coach of Canada's men's national team from 1998-2004 and was the first Canadian-born coach in the NBA when he joined the Raptors' staff in 2002. As a player Triano was a member of the Canadian national team from 1978-88 and played two professional seasons in Mexico and one in Turkey.