She wrote: "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."
The former "It girl" and reality TV star was found dead in her west London flat last week.
Her funeral is due to be held on February 27.
In a statement her family have said: "We would like to thank the many people who have contacted us about Tara following her untimely death. It has been a source of great comfort to know how loved she was by so many people.
"Tara died peacefully in her sleep due to a perforated ulcer and peritonitis.
"Those that knew and were close to Tara knew that there was no retreat to a "dark place" as some have disappointingly sought to suggest. In the last few weeks Tara was happy, positive and making plans for when she recovered her health.
"As usual she had been busy with the friends and family she loved, and who loved her in return. She was in communication with her family and others of whom she was fond over her final weekend and had spent a lot of her time recording music and playing the piano in her apartment - a sure sign that she was happy and feeling good.
"Tara's funeral will be on the February 27. This will be a private moment for family and close friends to grieve and we would ask that our privacy at this time is respected. We will miss Tara very much and will never forget the joy, love and humour she bought to our lives."
Last year, she revealed her fear of dying after being diagnosed with a non-malignant brain tumour.
After finding out about the growth in her pituitary gland, she later spoke about also suffering with an auto-immune disease that caused tiredness, joint pain and acute anaemia.
In what is believed to be one of her last interviews, she told about her quest to "make her family proud again".
Following the news of her sudden death, her close friends the Prince of Wales and the Duchess of Cornwall were among the first to pay tribute.
Charles and Camilla said they were "deeply saddened and our thoughts are so much with the family".
What is a perforated ulcer?
When a stomach ulcer splits the lining of the stomach open, it is known as perforation.
This can be very serious, because it enables the bacteria that live in your stomach to escape and infect the lining of your abdomen (peritoneum). This is known as peritonitis.
In peritonitis, an infection can rapidly spread into the blood (sepsis) before spreading to other organs.
This carries the risk of multiple organ failure and can be fatal.
- Originally published in Telegraph UK
