The Pickering, Ont., native agreed to a four-year contract worth US$30 million, according to multiple media reports.
Deals can't become official until Thursday, when the NBA's free agency moratorium ends.
"#WeTheNorth here I come!!!!!" Joseph posted on his verified Twitter account.
The 23-year-old spent his first four NBA seasons with the San Antonio Spurs, helping them win the leaguer title in 2014.
"A sincere thank you to all the fans, RC, Coach Pop and the entire Spurs organization for all the support over the last 4 years," Joseph posted. "SA will always be close to my heart... had my first game and first championship here! #ThankYou #NextChapter"
Joseph played in 79 games this past season with the Spurs, averaging 6.8 points, 2.4 rebounds and 2.4 assists.
San Antonio selected Joseph 29th overall at the 2011 NBA draft out of the University of Texas.
"He's been a real warrior in the sense that he's played (point guard, shooting guard), and even (small forward) sometimes,'' Spurs coach Gregg Popovich told The Canadian Press in February.
"He developed his game offensively a little bit more each year. He's always been a hard worker and a blue-collar kind of guy that got the most out of his abilities, but he's gained more confidence offensively and done a wonderful job for us.''