The 36-year-old Stanojevic had to be released as Serbia's under-19 coach by the Balkan country's Football Association (FSS) to sign a two-year contract with Partizan several hours after Stevanovic stepped down.
"I have come back home because this is where I grew up as a player and I want to thank Partizan for the confidence they have vested in me," Stanojevic told reporters.
"I am very ambitious and I am looking forward to tackling all the problems the club has encountered, I know many of the players and I have complete faith in them," said the youngest manager in Partizan's history.
Stevanovic, who remained unbeaten in the league with champions and cup holders Partizan, came under pressure last weekend after a 0-0 draw at unfancied rivals Jagodina left the team four points behind city foes Red Star.
The Cup defeat by Vojvodina means Partizan are staring at a trophy-less season after winning two successive league and cup doubles during the time Stevanovic was assistant coach.
"I had a moral obligation to step down and I made my decision after a long night of thinking whether to carry on or not," Stevanovic said earlier on Friday.
"The chants by Partizan's faithful for me to leave reverberated in my head and I knew what to do because I have the utmost respect for the club's fans."
Stevanovic was forced to step down after only his first domestic defeat of the season, but Partizan's weaknesses came to the fore in the Europa League where they won one and lost five group matches after squeezing through the preliminary rounds.
"I've been under pressure for a very long time and so have the players, some of them just couldn't deal with it," Stevanovic said.
