The electoral authority says 95% of voters backed constitutional changes; critics say turnout was as low as 10%.
CAR is still in the throes of a civil war that has uprooted a third of all people from their homes.
President Faustin-Archange Touadéra is backed by Russian Wagner mercenaries.
Extra fighters arrived ahead of the referendum to provide security.
Wagner boss Yevgeny Prigozhin said hundreds of its fighters had arrived in the resource-rich country as part of “a planned rotation before the referendum”, according to the Afrique Media website linked to the Russian group.
Wagner forces have been accused of committing war crimes as they back President Touadéra in the fight against rebel groups who still control large swathes of the country.
They reportedly trade in the minerals and timber industries.
The proposed new law would scrap the current two-term limit and extend the presidential mandate from five to seven years.
It would also ban politicians with dual citizenship from running for president unless they renounce the other.
Campaign group Human Rights Watch says this stirs up memories of anti-Balaka militias who targeted Muslims for their perceived association with Séléka rebels in the 2013 conflict, which saw hundreds killed in a civil conflict that continues to this day.
Constitutional coup
Opposition parties and some civil society groups boycotted the referendum vote on 30 July. They termed the referendum a “constitutional coup” designed to keep President Touadéra in power for life.
They also say the election process lacked transparency and there was not enough consultation beforehand.
Under the changes, a new post of vice-president would be created, who would be appointed by the president. The Senate would be scrapped and parliament would be transformed into a single chamber.
The president and members of his United Hearts Party say they are following the “will of the people”.
