The 29-year-old was club captain for the Greek champions and had been a pivotal figure since joining in 2008.
However, last season saw Dimitris Siovas break into the first-team and Papadopoulos became a somewhat peripheral figure at the Karaiskakis Stadium.
The Greece international took the time to praise Olympiacos president Evangelos Marinakis, but revealed that his relationship with Spanish coach Michel was beyond repair after completing his move to Turkey.
"I want to thank wholeheartedly the president of Olympiacos, Mr Marinakis, and the management who respected my desire, despite strong disagreement, to leave the club for a new challenge," said Papadopoulos in an open letter on the club's official website.
"I thought seriously and I decided to leave the club, which as everyone knows I have struggled to become a member of recently, because I have never felt the appreciation and trust of the current coach.
"Thus I came to the point where getting along with him was no longer possible."
With Olympiacos having bolstered their defensive ranks with the signings of Eric Abidal, Arthur Masuaku and Alberto Botia during the transfer window, Papadopoulos' chances would have been further limited.
But the former Aris centre-back holds no ill-feeling towards the club and feels the team can continue to improve under the presidency of Marinakis.
"It's a fact that the team has raised its level and can reach even higher because the man in control loves the club and has a vision," he added.