"I would like to share with my friends that I and Digvijaya Singh have married in a solemn ceremony, as per the Hindu rites," Rai said on social networking site Facebook on Sunday.
Sixty-eight-year-old Singh, who is former Madhya Pradesh chief minister and Rajya Sabha MP, had made public their relationship in April last year after some personal photographs of the couple were leaked online. Rai had then said that she had already filed for mutual consent divorce from her husband.
"We have also later registered our marriage," Rai, who works with Rajya Sabha TV, said on Sunday.
Rai said that the last one and a half years have been "particularly stressful and traumatic" for her. I was the victim of a cyber crime, but was treated as a criminal. I was trolled and abused in most derogatory language for no fault of mine.
"...I kept a dignified silence and went on with my work, believing in myself and my love for Digvijaya," she said.
Rai, 44, said while questions have been raised on their age difference, "I sincerely feel that at my age I know what is good for me and I can take my decisions as per my own wisdom."
"I have married Digvijaya Singh for love. Therefore, I have already requested him to transfer all his property and belongings to his son and daughters. I only want to embark on this new journey with him, working towards a dignified, professional career," she said.
The Congress general secretary, who is currently in the United States, has confirmed his marriage to Rai, Aaj Tak TV channel reported, adding Singh has said that he would speak after returning to the country.
Singh was married to Asha Singh who died in 2013 after battling cancer and they have four daughters and a son.
Image: Amrita Rai works with Rajya Sabha TV
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