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7 year oldThe star, who rose to fame in the 1990s as a hard-partying "It girl", received treatment in 2016 for a non-malignant brain tumour.
The Met Police confirmed a woman in her 40s was found dead at Palmer-Tomkinson's flat in Bramham Gardens, South Kensington, at 13:40 GMT.
Prince Charles, a close friend of the star's family, led tributes and said he was "deeply saddened" by her death.
Palmer-Tomkinson, a former Sunday Times columnist and reality TV star, was a regular on the London party scene in the 1990s and 2000s.
She made headlines for her social life, frequently appearing in the pages of society and celebrity magazines, before later appearing on reality TV.
The tabloid darling also battled a high-profile cocaine addiction, which she discussed publicly on a number of occasions.
She was diagnosed with a tumour last January after returning from a skiing trip and was also suffering from an auto immune disease that caused acute anaemia, tiredness and joint pain.
Life in pictures: Tara Palmer-Tomkinson
She had voiced fears that she might die, but hit back at critics who blamed her frail health on her well-documented troubles.
Speaking in 2016, she said: "That's always their [press] take on it... cocaine.
"That was so many years ago. But not many people can contemplate Tara's life without it".
As well as being a socialite, Palmer-Tomkinson was also a close friend of Prince Charles and attended the wedding of the Duke and Duchess of Cambridge in 2011.
In a tribute, the Prince of Wales and the Duchess of Cornwall said their "thoughts are so much with the family".
Television host and former Daily Mirror editor Piers Morgan paid tribute in a tweet that read: "RIP Tara Palmer Tomkinson, 45. A fun, feisty woman who battled many demons. Very sad news."
Majesty magazine editor and royal historian Ingrid Seward told BBC News: "She did have it all, and perhaps that was part of her problem.
"She was a good-looking girl, she had a fabulous family, she was a brilliant skier, rider, and she was very artistic. She sang beautifully."
She added: "I just think there was just too much, and life gave her too many choices, and she just didn't make the right ones.
"But she was a very generous, sweet person, I mean she really was a charming, charming girl."
Later in her career Palmer-Tomkinson appeared on reality TV series I'm A Celebrity... Get Me Out Of Here! in 2002, as well as several other TV shows.
Her father Charles was a former Olympic skier who taught Prince Charles.
The family was skiing with the prince in the Alps in 1988 when they were hit by an avalanche that killed one member of their party, Major Hugh Lindsay, and left Palmer-Tomkinson's mother Patti with serious leg injuries.
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