It consisted of three members of the government chosen by the Council of National Unity (Rada Jedności Narodowej), a rump parliament in exile.
It was created in 1954, after President August Zaleski declined to leave his office after his seven-year term ended.
According to the Polish April 1935 constitution, the legal basis for the existence of the government in exile, the president was allowed to choose his successor "during a war, in case his office falls vacant before the peace treaty is signed".
The post-war Akt Zjednoczenia Narodowego (National Unity Act) was an agreement among all the major political parties that assumed that presidents were to choose their successors every seven years, but that was rejected by Zaleski.
The Rada Trzech ceded its powers to Zaleski's successor, Stanisław Ostrowski.