The state-possessed TV declared the sackings on Monday evening, without giving reasons for President Kiir’s decision.
Gen Yol, nicknamed Tiger, was the commander of the presidential guard, before he was appointed the army chief of operations, training and intelligence last year.
He was blacklisted by the UN Security Council in 2015 for alleged war crimes and crimes against humanity committed during the onset of war in December 2013 against members of the the Nuer ethnic group.
Mr Dau was appointed Finance minister in 2016, with the hope of improving South Sudan’s straining economy. However, the economy of the young nation has never been stable, especially since the 2015 devaluation of the South Sudanese Pound.
Former technical advisor at the Ministry of Trade Salvatore Garang Mabiordit, was named the new Finance minister.
South Sudan attained independence in 2011 following a referendum whose outcome favoured the separation from Sudan with than 98 per cent approval.
However, it soon descended into another round of conflict pitting President Kiir’s loyalists and those allied to his former deputy Riek Machar.
The current phase of the South Sudan war has claimed more than 100,000 lives, according to the International Crisis Group.
Over 2 million South Sudanese have become refugees in neighbouring countries and another 1.9 million others remain internally displaced, according to the UN.
The war has also caused one of the world’s worst humanitarian crises after the Rwanda 1994 genocide, the UN added.
Multiple human rights abuses have also been documented by various groups.