The international community condemned the overthrow, but diplomats and analysts said it could create an opportunity to hold elections that were postponed by Tandja's unpopular constitutional reform in 2009.
It is likely the new military government will be under pressure from the international community to restore the rule of law and hold elections in the medium term, said Samir Gado, Vice-President of Rencap Securities.
The head of the military junta that seized Tandja during Thursday's gunbattle called for calm and said the work of government ministers and regional governors ousted in the coup was being done by their secretary generals.
After months of political wrangling over Tandja's amendment of the constitution, which provoked international sanctions and demonstrations, there was a sense of relief and hope for change in the uranium-producing west African desert nation.
I hope the soldiers restore some order ... clean up the political environment, said taxi driver Moussa Issa.
We need to start from scratch, without being compromised by the current political class which has been discredited over the last 20 years.
The junta, calling itself the Supreme Council for the Restoration of Democracy (CSDR), gave no indication of how long it intended to hold power but called on Niger's people and other countries to support its actions.
Its fighters on Thursday captured Tandja and his ministers in a four-hour gunbattle, before it suspended the constitution and dissolved all state bodies. At least three people were killed.
The president of the CSDR has been identified as Salou Djibo, an officer trained in Ivory Coast, Morocco and China who has served in U.N. peacekeeping missions.
Other leaders of the coup include Colonel Djibril Hamidou, a former spokesman for a junta responsible for the last coup in 1999, paving the way for elections that brought Tandja to power.
The coup operation was led by Colonel Abdoulaye Adamou Harouna, who commands Niger's standby force for West African regional bloc ECOWAS, military sources said.
OPPORTUNITY AFTER COUP?
Tandja drew criticism and sanctions after dissolving parliament and orchestrating a constitutional reform in 2009 that gave him added powers and extended his term beyond his second five-year mandate, which expired in December.
The reform removed most checks on his authority, abolished term limits, and gave him three more years in power without an election. Tandja justified it by saying he needed extra time to complete large-scale investment projects.
ECOWAS, which has for months tried to broker a solution to the deadlock between Tandja and the opposition, has already said it would punish any unconstitutional power-grab.
The Chairman of the African Union Commission, Jean Ping, said on Friday it called for the speedy return to constitutional order and affirms the readiness of the AU, in close collaboration with ECOWAS, to facilitate such a process.
U.S. State Department said on Thursday Niger required elections.