Governor Peter Underwood has passed away over night.
Government House advised of the 76-year-old's death early this morning.
''It is with great sadness that I advise that His Excellency the Honourable Peter Underwood AC, Governor of Tasmania, died last evening in the presence of his family,'' a release said.
''His family wish to express their deep gratitude for the care he received at the Royal Hobart Hospital and prior to that at Calvary Hospital Hobart.''
He was admitted to hospital last month to have a kidney tumour removed.
He was expected to make a full recovery.
However, he required more surgery and on Thursday, his official secretary David Owen said he had experienced a ``significant post-operation setback''.