Winning the referendum allows Correa to push ahead with initiatives such as ending the lease on a US military base, re-negotiating oil deals and restructuring the national debt.
In the past he has scared foreign investors with threats to stop making debt payments and promised to cut off contact with the International Monetary Fund.
But some economists predict that investors will welcome Correa's victory, as strengthening the presidency would mean Ecuador's leader will feel less pressure to maintain his approval ratings by implementing policies such as slashing debt payments and consequently push Ecuadorean bond prices higher.
Critics of Correa say he is centralising power around himself and could become too powerful.
But Ecuador's politics are volatile, the country has seen eight presidents in a decade, three of them toppled by public action, and the landscape could change again by September when another election will be held to select 130 members for the assembly.
Lucio Gutierrez, Ecuador's former president who was toppled from power by massive street demonstrations in 2005, remains a political influence and has vowed to use the 130-member body against Correa.
"I will defeat him in the assembly," he said on Ecuadorean television after the exit poll result.
Voting is mandatory for Ecuadoreans and Sunday's turnout appeared as high as for last year's presidential election.
Correa had staked his political career on the vote, pledging to resign if he failed to win emphatically.