In a televised statement, the coup leaders said they had suspended the constitution and dissolved the government.
Tiani was the head of the presidential guard that shut Bazoum in his palace on Wednesday, then declared it had ousted him because of poor governance and worsening security.
The general appeared on state television on Friday, described as the president of a newly formed military council, the National Council for Safeguarding the Homeland (CNSP).
"The President of the CNSP is the head of state. He represents the state of Niger in international relations," said a statement read by an officer.
The constitution has been suspended and the government dissolved, and the CNSP will exercise all legislative and executive power, according to the statement.
While the motives of the coup leaders remain unclear, it is rumoured that they were driven into action by an attempt to force out Tiani, who is also known by the name Omar Tiani.