USA Today said the contract was for five years and $15 million.
Ujiri, a native of Nigeria, has been general manager of the Denver Nuggets since 2010. He is the first African-born general manager in the history of the NBA and was recently named the league's executive of the year for the 2012-13 season.
"To come back to the Raptors, to live in such a great city and work in an organization that has committed all the resources necessary to win championships was a huge factor in the decision," Ujiri said.
Ujiri, 42, worked for Toronto as director of global scouting in 2007 and assistant general manager from 2008-10.
Toronto went 34-48 this season, the franchise's fifth straight losing record. The Raptors have not been in the playoffs for five years.