Mr Correa was rescued after soldiers opened fired on dissident police.
Moments after being freed he appeared on the balcony of Quito's presidential palace and spoke to thousands of cheering supporters.
He thanked the crowds and said he had just lived through the saddest day of his government.
The violence came after dark on a day of unrest in Ecuador that the president and his supporters said amounted to an an attempted coup.
Mr Correa had been holed up in the police hospital, where he was treated after being hit by tear gas in a confrontation.Hundreds of police, angry over a law that would cut their benefits, appeared to have prevented him from leaving the clinic.
Under cover of darkness Mr Correa was reportedly smuggled out of the hospital in a wheelchair even as a gunbattle between troops and police was under way.
Unrest had been reported across Ecuador on Thursday amid anger at a new law cutting benefits for public servants.
Speaking to his supporters, Mr Correa said he hoped the events of the day would serve "as an example to those who want to bring a change and stop the citizens' revolution without going through the polls".
Mr Correa said at least one police officer had died during the gunbattle at the clinic. Earlier there had been unconfirmed reports that one person had been killed and several injured during the unrest.
There are unconfirmed reports that a second army operation against dissident police is still under way in Quito.
'Kill the president' The drama began on Thursday morning when members of the armed forces and police angry at the austerity measures occupied several barracks and set up road blocks across the country.
TV stations showed images of police setting tyres on fire in the streets of Quito, Guayaquil and other cities. The National Assembly building was also occupied.
Police also took control of Quito's international airport for several hours.
In an emotional speech to soldiers from Quito's main barracks, President Correa tore at his shirt and said: "If you want to kill the president, here he is. Kill him, if you want to. Kill him if you are brave enough."
Moments later Mr Correa was forced to flee the barracks wearing a gas mask shortly afterwards when tear gas was fired by the protesters.
The president was later treated for the effects of the gas at a police hospital. His supporters said that dissident officers were preventing him to leave the clinic.
Mr Correa has blamed the Patriotic Society Party (PSP), led by Lucio Gutierrez, for fomenting the unrest, and said "all bad elements" in the police force would "be removed".
During the day Mr Correa received strong support from governments throughout the Americas, with a string of Latin American nations and the US all speaking up for the embattled president.