Panathinaikos announced both parties had agreed to the move and Obradovic released an open letter to the team's supporters via the club website.
"When I came in June 1999 to Athens to join Panathinaikos, I could not have imagined that this would be my team, my family, my home for 13 years," said the Serbian coach.
"In these 13 years, we had many beautiful moments, many celebrations, but also difficulties. We were always together as a great and true family.
"Now I have had a very difficult decision to take, that the collaboration of all these years is over," he added.
"I feel at this time that my decision is the best for everyone."
Obradovic won five Euroleague titles with the club, starting in his very first season.
That trophy haul is more than any other European club has won since 1978 and two more than any other team in the Euroleague Final Four era, which started in 1988.
Obradovic also led Panathinaikos to unprecedented domestic success, winning 11 league titles and the Greek Cup seven times. Overall, they won 23 national titles in 13 years.
Although they won the Greek Cup this season, the Greens surrendered the league title to arch rivals Olympiakos while they also exited the European Cup at the semi-final stage.