The Raptors offered the job to Rajakovic on Saturday and the sides are finalizing a contract that's expected to be completed soon, sources said.
Rajakovic, a native of Serbia, emerged out of an exhaustive process to sell Raptors president Masai Ujiri and general manager Bobby Webster on his candidacy to replace Nick Nurse.
Rajakovic's hiring leaves the NBA with no more head-coaching openings.
Rajakovic arrived from Serbia in 2012 as a G League head coach with the Oklahoma City Thunder before advancing onto the OKC bench and making stops with the Phoenix Suns and Grizzlies. He eventually elevated into Taylor Jenkins' top assistant with the Grizzlies.
The Raptors wanted a coach whom they believed could coach a contending team should the franchise stay on its current path with veterans, or a rebuilding roster should they eventually transform the roster to younger players and draft assets, sources said.
Golden State's Kenny Atkinson and Milwaukee's Charles Lee were other coaches given serious consideration in the process, sources said.
Toronto dismissed Nurse after going 41-41 this season before losing to the Chicago Bulls in the 9-10 game of the Eastern Conference play-in tournament.