A post mortem examination has found that Charles Kennedy died of a major haemorrhage linked to his alcoholism.
The former Liberal Democrat leader's family says it was an illness he "could not conquer".
The 55-year-old's body was found at his home in Fort William on Monday.
His family issued a statement:
"Charles' family would first like to thank the public and politicians who have been so warm in their tributes to him and so sincere in their concern for us.
We have been touched beyond measure by the outpouring of warmth for a man whose loss we will feel deeply forever.
The pain we feel has been at least eased somewhat by the reaction of so many people across Scotland, the UK and beyond, and by the affection expressed by politicians across the spectrum.
It has become all too apparent to us how much Charles meant to so many people and how many lives he touched.
We were grateful that his young son Donald was able to attend the Commons session where so many MPs spoke so warmly about his father.
The words and images of that day, and of so many other tributes, will be there for us to look back on with pride in Charles, and Donald will always know what a special father he had.
We would also like to thank all the public authorities and emergency services who have dealt with the aftermath of Charles' death with such courtesy, kindness and efficiency.
We have now been informed by the office of the Procurator Fiscal of the findings of the post-mortem.
Charles' death was caused by a major haemorrhage and the report makes clear this was a consequence of his battle with alcoholism.
We are grateful to the many friends and also medical experts who sought to help down the years but ultimately this was an illness Charles could not conquer despite all the efforts he and others made.
We can now proceed to make arrangements for his funeral and we will make an announcement on the details in due course."
Sky's Political Correspondent Anushka Asthana says Mr Kennedy admitted to a drink problem 9 years ago.
