Singleton has signed for the Betfred Super League newcomers on a three-year contract.
He will be joined in Toronto by scrum-half/hooker James Cunningham who has signed for Wolfpack from London Broncos on a two-year contract.
The 26-year-old Cumbrian made his Rhinos debut in 2011 and played 178 times for the club.
His 20 tries included one in the 2015 Challenge Cup final win over Hull KR at Wembley.
He also played in Leeds' 2015 and 2017 Super League victories.
Rhinos director of rugby Kevin Sinfield said: “Brad has been an outstanding servant for the Rhinos.
"He came through our academy and played a big role in the team as a Grand Final and Challenge Cup winner.
"It was felt that this was the right time for all parties that Brad was allowed to leave to pursue new challenges away from the club.
“We wish Brad the best of luck for the future at Toronto.
"He leaves with our best wishes and our thanks for all he has given to the club.”
The move will reunite Singleton with former Rhinos coach Brian McDermott, who is now in charghe of Toronto and his ex-teammate Anthony Mullally.
Wolfpack head of rugby Brian Noble said: “Both James and Brad are incredibly hard workers on and off the field and we are thrilled to have been able to secure their signatures.
"We are always looking for ways to strengthen our squad and this announcement certainly does that.
"They are proven performers at the highest level, we look forward to seeing James and Brad blend into our environment quickly as we prepare to launch our maiden Super League campaign.”