"After sharing a significant part of our lives together, we have decided to part ways with mutual understanding and respect," the statement read.
The couple said their relationship would continue as a friendship and that their children's happiness and well-being would remain their priority.
"Though our marriage has come to an end, we remain good friends and devoted parents to our wonderful children. Their happiness and well-being will always be our shared priority."
They also asked for privacy as they deal with the change in their personal lives.
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"During this personal transition, we seek your understanding, kindness and respect for our privacy. We extend our heartfelt gratitude to everyone who has stood by us throughout this journey," they added.
No reason given for separation
Neither Kalyan nor Anna has spoken about what led to their decision to separate. The joint statement does not mention divorce proceedings or any arrangements concerning their children.
Kalyan is currently the Andhra Pradesh Deputy Chief Minister. Anna is a Russian citizen.
Kalyan and Anna got married in 2013. They have two children together, a daughter, Polena Anjana Pawanova, and a son, Mark Shankar Pawanovich.
The separation marks the end of Kalyan's third marriage.
He was previously married to Nandini in 1997. The two separated in 1999.
Kalyan later married actor Renu Desai in 2009. They have two children, a son, Akira Nandan, and a daughter, Aadhya. Their marriage ended in divorce in 2012.