"Olympiakos FC and James Rodríguez have decided to terminate their cooperation," the club said in a statement. "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."
Olympiakos are six points behind joint leaders Panathinaikos and AEK Athens in the Greek league and lost to AEK 4-2 on aggregate in the Greek Cup semifinals.
"I would like to thank everyone for all the time that we have spent together," Rodriguez wrote on Twitter.
"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, who won the Golden Boot with Colombia at the 2014 World Cup, has played for three clubs in as many years since leaving Real Madrid in 2020, having also spent single seasons at Premier League club Everton and Qatari side Al Rayyan.