The new president was sworn in at a ceremony in Brasilia amid the highest security ever for a presidential inauguration in the largest and most populous nation in Latin America.
Bolsonaro was stabbed and severely injured during the campaign, undergoing surgery, with more surgical intervention planned. Since then, security around him has been significantly increased.
Anti-aircraft laser-guided missiles were mobilized and thousands of officers were involved in the security effort.
The inauguration crowd, which the government estimated to number some 115,000 people, was not allowed to get too close to the presidential palace.
Protocol calls for the Brazilian president to make two speeches, one in Congress and one to the people. In his speech to lawmakers, Bolsonaro said he was determined to fight corruption, crime and "ideological submission."
"I want to take this opportunity to call on each congress member to help me in the mission to restore and rebuild our nation, freeing it from corruption, crime ... and ideological submission," he said.
"The government will not spend more than it takes in," he added.
In his speech to the general public, he highlighted his concerns about crime, for which he received applause.
Bolsonaro has always taken a pro-gun stance and said last week that he will relax gun laws to allow anyone without a police record to own a gun.
"Our concern is the safety of good citizens, and the guarantee of property and self-defense. Our commitment is to value and support the work of all security forces," he said.
First Lady Michelle Bolsonaro also addressed the people, delivering her speech in sign language.
The first lady, who is involved in a campaign to promote the inclusion of people with hearing disabilities, said deaf people will not be forgotten by her husband's administration.
Several foreign leaders attended the presidential inauguration ceremony, including Israel's Prime Minister Benjamin Netanyahu and the presidents of Paraguay, Uruguay, Bolivia and Honduras.