Author Santa Montefiore posted a series of tweets thanking people for their support following Ms Palmer-Tomkinson's death at the age of 45.
She was found dead at her flat in South Kensington last week.
Ms Montefiore said a coroner found Ms Palmer-Tomkinson had died of "natural causes" and "did not have a brain tumour".
She said: "Tara's good friends & family know that she was in high spirits in her last days. She had plans, trips & had written a moving new song."
There was no retreat to a "dark place" and Ms Palmer-Tomkinson was "happy and positive" before her death, her family said in a statement.
Life in pictures: Tara Palmer-Tomkinson
Ms Palmer-Tomkinson rose to fame in the 1990s as a hard-partying "It girl". She received treatment in 2016 for a non-malignant brain tumour.
She used her celebrity status to raise the profile of brain tumours by speaking publicly about her ill-health.
A former Sunday Times columnist and reality TV star, she 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.
She also battled a high-profile cocaine addiction, which she discussed publicly on a number of occasions.
Palmer-Tomkinson 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.
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".
Ulcers are caused when acid used to digest food damages the stomach's lining - often as a result of bacteria or the use of certain medicines.
Complications  are relatively uncommon, but they can be very serious if they do occur.
If a stomach ulcer splits, known as perforation, bacteria that live in the stomach escape and infect the lining of the abdomen.
In peritonitis, as it is known, an infection can rapidly spread into the blood before spreading to other organs.
This carries the risk of multiple organ failure and can be fatal if left untreated.
Source: NHS Health A-Z
As well as being a socialite, she 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".
A private funeral will be held on 27 February, her family said.
Socialite Tara Palmer-Tomkinson died "peacefully in her sleep" from a perforated ulcer, her sister said.