Mr Macleod, 63, was being treated for cancer at Gartnavel Hospital in Glasgow.
He was an award-winning writer and well-known broadcaster who regularly contributed to BBC political programmes.
His death has been described as a “huge loss to journalism”.
Scotland Secretary Alistair Carmichael said: “The passing of Angus Macleod is sad news. My thoughts and sympathies are with his family and his many friends.
“His passing will leave an enormous void in their lives and the lives of everyone with an interest in Scottish politics and public life.
“Angus was a journalist of the old school. He was a real inquisitor. His knowledge of our politics was matched by very few.
“Every politician knew a call from Angus would bring searching questions which would demand an answer. It was, however, never an unwelcome call.
“He was a true gentleman who brought an authentic Highland flavour to our politics. He will be missed.”
Former Chancellor and leader of the Better Together campaign Alistair Darling said: “Angus was a gentleman in every sense of the word. He is a huge loss to journalism. Our thoughts are with his family.”
Many expressed their thoughts on Twitter. Deputy First Minister Nicola Sturgeon described him as “a journalist of the old school and undoubtedly one of the best. Rest in peace”.
First Minister Alex Salmond wrote: “Saddened to hear Angus Macleod has passed away. A thoughtful and insightful journalist who will be missed right across the political divide.”
Scottish Conservative leader Ruth Davidson said: “Just turned on Twitter and learned of the passing of Angus Macleod. Incredibly sad. He was wonderful and irascible in almost equal measure.”