He took the oath of office in a ceremony at the National Stadium attended by an estimated 30,000 people yesterday.
Hernandez, 45, a lawyer, inherits a deeply divided country of 8.5 million people where 71 per cent of the population lives in poverty and a spiralling homicide rate has reached 20 murders per day, one of the highest in the world.
"The party is over for criminals," Hernandez said after his swearing in, adding that he would allow "zero tolerance on crime" and "reduce homicide more" in the coming months.
Hernandez invited US President Barack Obama and the US Congress to recognise their "common, but different responsibilities" on drug trafficking, one of the main factors behind Honduran violence, calling for both countries to "work together."
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"Seven out of ten homicides are drug-related... Which means that if there were no drug problem, we would not be among the most violent countries in the world," he said.
Hernandez replaces Porfirio Lobo, of the same National Party.
The country's supreme court last month rejected an appeal to overturn November's presidential election results, which the leftist Libre party claimed was stolen by fraud.
Libre candidate Xiomara Castro, wife of party leader and ex-president Manuel Zelaya, officially lost to Hernandez, garnering just 29 per cent against 37 per cent. She described the results as a "disgusting monstrosity."
Some 5,000 protesters led by Zelaya protested yesterday in Tegucigalpa during the swearing in.
The move led to 100 days of unrest that included massive street protests and a crackdown on leftist activists.