Rodriguez joined the Greek giants back in September as a free agent after leaving Qatari side Al Rayyan.
The 31-year-old made 23 appearances during his short spell at Olympiacos, scoring five goals and providing six assists but both parties have still decided to go their separate ways.
A statement from Olympiacos read:" James will always be part of our club and a member of the 'red and white' family. We want to thank him for his service and we wish him every success in the future."
In his own message on social media, James said: "I would like to thank everyone for all the time that we have spent together.
"Although we are going our separate ways, I feel that I will always be a member and welcomed in the family of the great port Piraeus. I wish all the best to Olympiacos and every success in the future."
Rodriguez rose to prominence at the 2014 FIFA World Cup in Brazil, where he emerged as top scorer with six goals.
He earned a move to Real Madrid on the back of those performances but has struggled to find stability in recent years, failing to last a season at Everton, Al-Rayyan and Olympiacos.
