Under the current constitution, the president has been unable to seek re-election because he is over the age of 70 and has already served two terms.
The opposition say turnout was low and the vote should be annulled.
However, official results put the turnout in Sunday's referendum at 72%.
More than 1.2 million people voted in favour of the change - 92.3% of voters - while nearly 102,000 rejected it, the electoral commission said.
The opposition called for a boycott of the poll and one of its leaders described the official results as a "fraud".
"From what we could see on the day of the vote, the announcement that turnout was more than 72% is extremely scandalous," Clement Mierassa told the AFP news agency.
President Sassou Nguesso, 71, is one of Africa's longest-serving rulers, first coming to power in 1979 and ruling until 1992 when he lost elections. He returned as president in 1997 after a brief civil war and has since won two elections.
He is now coming to the end of his second seven-year term.
Tens of thousands of people took part in a peaceful demonstration against the referendum in September.
Four people died last week, when security forces dispersed angry protesters in the capital, Brazzaville, and the economic hub of Pointe-Noire.
The election is due to take place in 2016.
Africa's longest-serving leaders:
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The review follows the attack in the French city of Nice on 14 July which left at least 84 people dead.
The government said that the measures may make attending the games less comfortable for visitors but they would result in greater security.
The Games are expected to attract as many as 500,000 foreign visitors.
"The attack in Nice is worrisome for us too. We will review procedures, make more barriers, more spot-checks on visitors and roadblocks", said Defence Minister Raul Jungmann.
The authorities had previously declared public holidays and banned trucks from certain areas of Rio during the Olympics to ease congestion and improve emergency response capabilities.
Rio's mayor, Eduardo Paes, said security would be beefed up for Olympic delegations from countries which have been targeted.
Mr Paes did not give any further details, but the head of French military intelligence said France had been informed of a planned terror attack on its team at the Rio Games.
Gen Christophe Gomart told a parliamentary commission in May that a "partner agency" warned of the plot by a Brazilian Islamist militant.
The transcript of the hearing was made public this week.
"Brazil is confident about its preparations. We are employing the most modern security and defence techniques", Sports Minister Leonardo Picciani told Reuters news agency.
Earlier this week, Mr Picciani said the armed forces would get an extra $24m (Â£18m) to help them meet security needs.
The military would begin patrolling sports venues from 24 July, he added.
More than 80,000 police and soldiers will patrol the streets of Rio for the duration of the games.
More than 92% of voters in Congo-Brazzaville's controversial referendum have approved constitutional changes to allow President Denis Sassou Nguesso to run for a third term, results show.
[NEXT_CONCEPT]
The Brazilian government has met to reassess security measures ahead of next month's Olympic Games in Rio de Janeiro.