Diana Campbell, 60, waited until high tide before steering the wheelchair from her home to the quayside and driving off the sea wall. The chair fell 20ft before hitting the water.
Miss Campbell drowned as she was swept out on the tide. Her body was later found several hundred yards away, washed up on the foreshore. The wheelchair was also recovered.
Miss Campbell, a niece of the explorer Sir Cecil Rhodes, had been disabled by arthritis since she was a teenager.
However, her love of the sea triumphed over her disability and she became a keen sailor, voyaging around the world on yachts. She also helped to design a Challenger yacht, specially produced for disabled people to crew.
A spokesman for Hampshire Police said that the alarm was raised early yesterday when a friend of Miss Campbell's called at her home and discovered that the patio doors at the rear were wide open.
Inside the house, several letters were found, one of them addressed to the local coroner.
The spokesman confirmed that the friend had said Miss Campbell was suffering from terminal cancer but had refused to take any medication. An inquest will be held.