The Hollywood star said she took the decision to have the procedure when doctors told her she had an 87% risk of breast cancer and a 50% risk of ovarian cancer.
Angelina Jolie has had a preventive double mastectomy
Writing in The New York Times, the Tomb Raider actress said she finished the three months of medical procedures on April 27, and added: "During that time I have been able to keep this private and to carry on with my work."
The 37-year-old star said she was writing about the ordeal, in an article titled My Medical Choice, in the hope that other women can benefit from her experience.
Angelina praised her 'loving and supporting' partner, Brad Pitt
Jolie, whose mother had cancer and died at 56, said waking up from the operation can feel "like a scene out of a science-fiction film" .
She said the decision to have the mastectomy was not easy but that she was happy to have gone ahead with it.
"My chances of developing breast cancer have dropped from 87 percent to under 5 percent. I can tell my children that they don’t need to fear they will lose me to breast cancer.
It is reassuring that they see nothing that makes them uncomfortable. They can see my small scars and that’s it. Everything else is just Mommy, the same as she always was.
"And they know that I love them and will do anything to be with them as long as I can. On a personal note, I do not feel any less of a woman. I feel empowered that I made a strong choice that in no way diminishes my femininity."
Urging women to get checked out, the star said: "For any woman reading this, I hope it helps you to know you have options.
"I want to encourage every woman, especially if you have a family history of breast or ovarian cancer, to seek out the information and medical experts who can help you through this aspect of your life, and to make your own informed choices."
Paying tribute to Pitt, Jolie said: "I am fortunate to have a partner, Brad Pitt, who is so loving and supportive.
"So to anyone who has a wife or girlfriend going through this, know that you are a very important part of the transition.
"Brad was at the Pink Lotus Breast Centre, where I was treated, for every minute of the surgeries.
"We managed to find moments to laugh together. We knew this was the right thing to do for our family and that it would bring us closer. And it has."
Michelle Heaton hailed Jolie's decision to publicise her double mastectomy as "incredibly important" in giving support and encouragement to other women in a similar situation.
Libery X star, Michelle Heaton underwent a double mastectomy last year
"I can't even stress how much of an impact I had, saying that I was going through this, on women - especially through Twitter and people writing to me.
"It was such a huge impact and I know that I have had hundreds of women who have gone for this test and subsequently found that they had the BRCA gene and they can then make an informed decision," she told ITV's Daybreak.
"Imagine what impact somebody as huge as Angelina Jolie can have on this."
Foreign Secretary William Hague, who in March visited refugee camps in the Democratic Republic of Congo with Jolie as part of a campaign to highlight the problem of mass rape in conflict areas, said she was "a brave lady" who would be "an inspiration to many".
Hague told Sky News: "She is a courageous lady and a very professional lady. She's done a lot of work with me in recent months.
"She also came over to the G8 foreign ministers' summit in London to work with me on our initiative on preventing sexual violence in conflict and travelled with me through some difficult places in the Congo.
"She gave no sign that she was undergoing such treatment and I think she's a very brave lady, not only to carry on with her work so well during such treatment, but also to write about it now and talk about it. I think that she's a brave lady and will be an inspiration to many."