Gen. Tiani formally established the transition bodies during two ceremonies that were broadcasted on state television.
Thursday's proceedings witnessed members of the two bodies swearing an oath in front of Tiani as he made his first appearance since leading the July 26 ousting of democratically elected President Mohamed Bazoum.
Military chiefs, government members, traditional chiefs, religious figures and foreign diplomats attended the inaugurations in the capital, Niamey.
The new state court replaces the court of cassation and state council, which were dissolved after the coup, according to the order setting out public powers during a transition period leading to elections.
For now, the junta has demanded up to a three-year transition back to civilian rule, but no date has been fixed for elections.
The anti-corruption commission's main role will be recovering all illegally acquired and misappropriated public property.
It is made up of judges, army and police officers and representatives of civil society.
Tiani has promised to hold a national dialogue, which will help determine how long the transitional period will continue.
Bazoum has been held at his residence in the heart of the presidential palace since his toppling.
Niger has been subject to heavy economic sanctions by the Economic Community of West African States, ECOWAS since the coup, driving up inflation and leading to shortages of some products including medicines.