The vote by lawmakers in both houses amends the Constitution's presidential term definition and also turns the presidential election into a single round.
The national assembly and senate held a joint session in the capital Libreville where 85 percent of votes backed the proposal, "well above the qualified majority of two-thirds required," said assembly speaker Faustin Boukoubi.
The amendments bring all mandates in line at five years and make all elections single-round ballots again after the last changes to the Constitution in 2018 set up two rounds of voting.
Prime Minister Alain-Claude Bilie-By-Nze said the outcome was the "result of a consensus after 10 days of political concertation between the majority and the opposition" in February.
Several senior opposition leaders and their parties had snubbed the talks.
Sections of the opposition criticized the changes, in particular the end of two rounds of voting, as a means of "facilitating the re-election" of Ali Bongo Ondimba.
Presidential, legislative and local elections are scheduled for the end of August, but a date still has to be announced.
In 2009, the now 64-year-old Bongo took over from his father Omar Bongo Ondimba, the oil-rich west African country's ruler for 41 years, and he is widely expected to run for re-election.
The president was narrowly re-elected in 2016 with just 5,500 votes more than rival Jean Ping who claimed the election had been fixed.
Bongo suffered a stroke in 2018 and spent months on the sidelines recovering, leaving the opposition to question his fitness to run the nation.
His powerful Gabonese Democratic Party (PDG) holds strong majorities in both houses of parliament and is pushing for the president to announce he will stand again.
The opposition has failed to agree on a single candidate for the presidential election, leaving some 15 candidates to announce their intentions to stand.
The Bongo family has ruled the country for 55 years already and is branded a "dynastic power" by the opposition.