Mr Fayose has denied reports that he had fled the country, saying he was in hiding because he feared for his life but remained governor.
His deputy Biodun Olujimi, who was also impeached, says she is now acting governor, although the state assembly has installed former speaker Friday Aderemi.
'Ridiculous'
President Obasanjo told national television that the governor's impeachment was "a clear case of usurpation of power."
"We have come to a sad, ridiculous and unacceptable situation in Ekiti where we have three governors."
"It is dangerous for our democracy to allow this flagrant violation."
Brigadier General Tunji Olorun (rtd), a former military state governor during military rule, has been appointed for six months has been sworn in in the capital, Abuja.
Ekiti State is only the second state to witness a state of emergency in Nigeria since President Obasanjo came to power in 1999.
Plateau State was placed under a state of emergency for nine months in 2004 after ethnic violence.
Governors under fire
On Monday, Ekiti State House of Assembly voted to remove Mr Fayose from power but several senior officials have condemned the impeachment.
The Nigerian Bar Association called for a boycott of Ekiti State courts until the matter was resolved.
Nigeria's remaining 35 governors met President Obasanjo and informed him that they would not accept Mr Aderemi at their Governors' Forum.
If the Ekiti State matter is not resolved, it could turn into a major crisis for the whole country, says the BBC's Mannir Dan Ali in Abuja.
Some senior Nigerian lawyers, however, say the impeachment reflected the "beauty of democracy".
Mr Fayose is the third governor to be impeached since Nigeria returned to multiparty democracy in 1999.
Two other governors are currently facing impeachment proceedings from their local legislatures over allegations of corruption.
Nigeria's anti-corruption agency says it is investigating two-thirds of the country's governors.
While Mr Fayose was being sacked, MPs in Anambra State began impeachment proceedings against Governor Peter Obi.
Early last week, Plateau State Governor Joshua Dariye was served with an impeachment notice in controversial circumstances that sparked riots in the central state.
Critics of President Obasanjo say his anti-corruption drive is a cover for a political witch-hunt.