Maduro, who had been vice president, said in his acceptance speech during a ceremony held in the National Assembly he would work to keep alive the memory and legacy of Chavez, CNN reported.
"We still have him in our hearts," Maduro said. "I have him here, here, as if he was the name in my soul, because I am his son.
"We are here to guarantee peace, safety and political stability and the lifting up of the poor in Venezuela will continue. Onward and upward with socialism!"
Madura appointed Science and Technology Minister Jorge Arreaza to be his vice president.
Maduro urged the opposition to field a candidate for presidential elections to be held in 30 days.
"Some of them are here today," he said. "Welcome.
"May the best person win. The people will decide."
Opposition leader Henrique Capriles, the governor of Miranda state, expressed disdain for Madura's inauguration, telling reporters it was "an abuse of power."
"To be president, the people have to elect you," he said. "The constitution is very clear."
Venezuelans waited for hours Friday to view Chavez's body as foreign leaders were escorted in through a side door.
Chavez, who died Tuesday at 58, lay in state at a military academy in Caracas, The New York Times reported. Some of those waiting to see him had been in line for more than 24 hours.
"I've been here since yesterday and to tell you the truth I don't feel tired," Genesis Briceno, 22, an economics student, told the Times Friday morning. "I want to see him."
Chavez's mother, Elena, was applauded when she arrived.
Raul Castro of Cuba, Evo Morales of Bolivia, Rafael Correa of Ecuador and Daniel Ortega of Nicaragua, all allies of Chavez in Latin America, came to Caracas. They were joined by Iranian President Mahmoud Ahmadinejad, who called Chavez a "dear friend of all nations worldwide," CNN reported.
"He was the emotional pillar for all the revolutionary and freedom-seeking people of the region and the world," Ahmadinejad said.
At least 50 countries were sending delegations to Caracas for Friday's funeral. The United States, which does not have an ambassador in Venezuela, is being represented James Denham, the charge d'affaires at the U.S. Embassy in Caracas, and by Rep. Gregory W. Meeks, D-N.Y., and former Rep. William Delahunt, D-Mass.
Venezuela is in a seven-day mourning period.
Maduro said Thursday Chavez's body will be embalmed and "surrounded by crystal glass forever, present forever, and always with his people."
"It has been decided to prepare the body of the president commander, embalming to be open forever ... as is Ho Chi Minh, as is [Vladimir] Lenin and Mao Zedong," Maduro said in a televised address, referring to Vietnamese, Russian and Chinese communist revolutionary leaders.
"The body of our commander in chief will remain embalmed at the Museum of the Revolution in a special way, so it can stay in a glass casket and our people can have him forever," he said.
After the mourning period, Maduro said Chavez's body will be taken to the Museum of the Revolution, in the building that was Chavez' 1992 headquarters when he led an unsuccessful coup against President Carlos Andres Perez.
Many Chavez followers have demanded Chavez be buried in the National Pantheon, the final resting place of Venezuelan heroes including Simon Bolivar, who helped overthrow Spanish rule in the early 19th century.