In late May, Madrid refused to recognize a cabinet proposed by Torra, which included exiled and imprisoned Catalan politicians.
Torra said the actions of the Spanish government broke the law and violated his political rights.
Nevertheless, the Spanish government approved Torra's second Cabinet list. Earlier on Friday, a decree on new regional government appointments was published in the Official Gazette of the Government of Catalonia.
The regional government is set to regain its autonomy and begin working on Saturday.
Earlier in the day, Rajoy was ousted by an absolute majority of 180 out of 350 lawmakers, with socialist leader Pedro Sanchez becoming a new prime minister.
The motion was initiated, following a recent court ruling, which found several officials of Spain's People's Party guilty of embezzlement, tax evasion and numerous other offenses. The party itself has been fined by Spain's High Court last week for its involvement in the "corruption scheme."
Responding to the accusations against him, Rajoy rejected the political proceedings as a plot by Sánchez and his party to undemocratically seize power.