The singer announced the sad news to fans on the first day of Breast Cancer Awareness Month.
"I was diagnosed with breast cancer for the second time earlier this year and am currently in the final stages of recovery after undergoing a double mastectomy," the I'm Outta Love songstress wrote.
"It has been an intense journey but I am feeling great and ready to start the next chapter."
The singer, who was first diagnosed with the disease in 2003, remained upbeat and determined to use her fame to help others facing breast cancer.
"Breast Cancer Awareness Month gives all who are facing this disease a chance to gain strength and support from each other," she said.
"Early detection has saved my life twice. I will continue to battle and lend my voice in any way I can."
Anastasia follows in the footsteps of Angelina Jolie, Sharon Osbourne and Michelle Heaton who have all undergone the procedure.
The One Day In Your Life singer had been due to begin touring in London on 6 April but was advised by doctors to cancel all performances and not to travel.
However, she announced in February that she had been diagnosed with breast cancer again and was forced to cancel the European tour.
"I feel so awful to be letting down all my amazing fans who were looking forward to It's A Man's World Tour," she said. "It just breaks my heart to disappoint them."