The left-wing leader and ally of the late Venezuelan President Hugo Chavez has a high popularity rating and his party controls Congress.
Mr Correa first took power in 2007 and will serve what he says is his last term until 2017.
A number of leaders from the region and Europe attended the inauguration.
Mr Correa was re-elected in February with more than half of the votes, and recent polls suggest his approval rating stands at around 90%.
Speaking after the ceremony, Mr Correa said his country is going through "profound political, social and economic changes."
"Between 2007 and 2012, we managed to make more than one million Ecuadoreans leave poverty behind," the President said.
The ceremony was attended by Venezuela's President Nicolas Maduro, the successor of Mr Correa's late friend and ally Hugo Chavez.
Among other heads of state and dignitaries at the inauguration were Bolivia's leader, Evo Morales, and Colombia's Juan Manuel Santos.
Correspondents say Mr Correa's main challenges are attracting investment and boosting trade.
His election in 2006 ended a long period of political instability in Ecuador.
But critics accuse Mr Correa of being a dictator in the making.
The 50-year-old US-trained economist has been accused of implementing policies that have served to strengthen his hold on power and erode the influence of political opponents and private media.
But his so-called "citizens' revolution" has made him popular with many ordinary Ecuadoreans and has won him friends among other Latin American left-wing leaders.
Since 2007, Mr Correa has re-written the country's constitution: a move that allowed him to run for, and win, a new term in 2009.
Ecuador's President, Rafael Correa, has been sworn into office for an unprecedented third term in the capital, Quito.