The winger had previously insisted he would never play for his country with Curcic in charge, after being left out of the games with Poland and Estonia.
Tadic refused to play for the 44-year-old after being left out of the international friendlies with Poland and Estonia last month, labelling his treatment as "humiliating and disrespectful".
But a series of bad results has culminated in Curcic leaving the hot seat, ending a six-year stint of working with the national team having previously worked as an assistant and caretaker coach.
He said in a statement released on the Serbian FA's website that the team's poor recent from, combined with the failure to qualify for Euro 2016, made his position untenable.
"Unfortunately, after some bad results, me and my staff have lost support and we have decided to leave our posts," he said.
"After a discussion with senior FSS officials, it was my assessment that the goal of qualifying for the 2018 World Cup lacks the right atmosphere and support.
"I wish to thank the players for their full commitment and those individuals who believed in my work, while I also hope Serbia will reach the tournament in Russia."
Former Aston Villa striker Savo Milosevic, who was one of Curcic's strongest supporters, has also left his position as national team director, which suggests there is likely to be a radically different approach to the team's World Cup 2018 qualifying campaign.
It means that Southampton star Tadic, who has previously been capped 35 times by his country, could now be primed for a return, with Serbia taking on Cyprus, Israel and Russia over the next few months.