The journalist, who wrote a memoir titled Shoot The Damn Dog, was seen going into the sea near her home in St Leonards-on-Sea, East Sussex, friends said.
Described as "smart, tough and stylish", Brampton, 60, was the launch editor of British Elle magazine at the age of just 30 and wrote an advice column for the Daily Mail, the Press Association reported.
Her writing about depression was hailed as frank and moving, and is credited for helping others through the illness.
In a piece in 2003 for the Daily Telegraph, Brampton revealed she had tried to kill herself a year earlier but since recovered, and that after developing depression she had told herself to "Get over yourself, it said. Stop snivelling. Stop complaining. Stop whining."
I began to emerge from the illness last summer. My recovery came in fits and starts. To begin with, I dared not even admit I felt happy, in case the sensation was snatched away. But I do feel happy - not all of the time, but at least some of it. I realise I do still have the capacity for joy. I look back at myself, at those years, in horror and sadness. It is as if I lost two years of my life.
I still get occasional black days, when the terror and hopelessness crowd everything from my mind and close down the world until it stops. On days like that, if my daughter is not with me, I go to bed. In that state, I would not wish myself on anybody.
I simply take the phone off the hook and hide. I keep a writing pad beside me, scribble down anything that comes to mind. It is my therapy and my cure. The other day, I looked at my scribbles and saw that I had written: "I find it very difficult to stay alive."
People paid tribute to Brampton on Twitter, calling her writing "tender" and the news of her death "incredibly sad":
In an obituary for Brampton, former Independent On Sunday editor Lisa Markwell says: "Sally’s skill extended beyond journalism and literature; she was the source of wise counsel that could be applied to all areas of life.
"In 2006 she was hired as agony aunt for the Sunday Times Style supplement. Her weekly column, Aunt Sally, responded to readers’ letters and her advice was unflinching.
Markwell added that her memoir Shoot The Damn Dog was "regarded as an important work on the subject but many media figures found it remarkable that this connected and successful woman could be a depressive.
"In his Observer review, Simon Garfield said that “she writes of her despair with such fluidity and lyricism that it is sometimes difficult to imagine her as the stumbling and empty figure she describes”.
Current British Elle editor-in-chief Lorraine Candy paid tribute, describing her as a "kickass boss" who nurtured new talent with the same enthusiasm as she nurtured her family and friends.
She wrote on its website: "Her legacy is a spirited brand that is as relevant today as it was 31 years ago because there are so many 'Sallys' out there."
Susan Ward Davies, who worked with Brampton on the launch of Elle in 1985, spoke of her as a "dynamic and very inspiring leader".
"Looking back, the Elle girl that Sally invented was such an optimistic role model, such an aspirational character and such a free spirit that you could never imagine the person who created her could have been afflicted with depression," she said.
Guardian journalist and fellow East Sussex resident Kathryn Flett said Brampton - who studied fashion at Central St Martins College of Art and Design - would be remembered by friends and readers for her humour, courage and wisdom.
Sussex Police have not made a formal identification of the body. A police spokesman said a woman's body was pulled ashore by a member of the public after being spotted at around 2.30pm on Tuesday.
An air ambulance landed at Galley Hill in Bexhill-on-Sea, near St Leonards, but she was pronounced dead at the scene. The coroner's office has been informed.
A Sussex Police spokesman said: "There are not thought to be any suspicious circumstances at this time and it is believed that the identity of the woman is known."