Sassou Nguesso has ruled the oil-producing nation for 31 of the last 36 years and the constitutional change makes it possible for the 71-year-old to win a further five-year mandate at an election due next year.
More than 92% of voters in Sunday's referendum supported the change and turnout stood at 72% of the more than 1.8 million registered voters, according to figures from the electoral commission.
More than 1.2 million people voted in favour of the change, while around 102,000 rejected it, the commission said.
The turnout figure was immediately disputed by the opposition, which had called for a boycott of the referendum.
Sassou Nguesso ruled the Central African country from 1979 until 1992, when he was defeated in a presidential election. His rule resumed five years later after his forces defeated the then-president in a brief civil war.
He is the latest African president to try to prolong his grip on power by changing the constitution. Several such initiatives have provoked violence, and four died in Congo last week when security forces opened fire on protesters.
Last October, Burkina Faso's leader of 27 years was toppled by protests and the president of Burundi won a third term in July amid violent protests. Rwanda and the Democratic Republic of Congo have also sought constitutional change.
Western governments are torn between endorsing veteran African leaders who often represent stability or pressing for term limits for the sake of greater democracy. The dilemma is exacerbated when leaders use constitutional democratic means that the West has advocated for Africa to prolong their rule.
Congo is a former French colony and France's President Francois Hollande said last week that Sassou Nguesso had the right to consult his people on the issue.
African leaders have often criticised what they see as meddling by foreign governments who express views on their internal politics.
A victory for Congo's government in Sunday's referendum was never in serious doubt, given the opposition boycott. But attention had focused on turnout, with the opposition hoping that low participation in the vote would undermine its credibility.
Senior opposition leader Pascal Tsaty Mabiala, secretary of the Pan-African Union for Social Democracy party, said on Tuesday that authorities had exaggerated the turnout figure.
"It (the result) is not legitimate. It is not credible. There is no way there could have been 70% turnout. For us, this result is a fantasy," he told Reuters.
At least 27 people were killed, including some on the ground, when a small plane crashed into a densely populated neighborhood in the city of Goma in eastern Democratic Republic of Congo on Sunday, a rescue official said.
3 years, 3 months ago
A former vice president of the Democratic Republic of Congo, Jean-Pierre Bemba, was sentenced on Tuesday to 18 years in prison for crimes against humanity and war crimes committed by militiamen under his command during a four-month rampage of looting, rape and murder in the Central African Republic.
6 years, 9 months ago