Jindal, whose first name is Piyush, is the son of immigrants from India and the first non-white Louisiana governor since the 1870s.
He will replace Kathleen Blanco, a Democrat who chose not to run in the election after she was widely criticised for a poor recovery effort in the wake of hurricane Katrina in 2005.
During his election campaign, Jindal promised to stop political corruption, cut taxes and improve schools.
“They can either go quietly or they can go loudly, but either way, they will go,” he said of those he accuses of corruption.
When he takes office in January, Jindal will become the country’s youngest state governor in office.
“I think the Jindal camp, almost explicitly, [wanted] to cast it this way: If you were able to re-vote, who would you vote for?” Pearson Cross, a political scientist at University of Louisiana at Lafayette, said.
Jindal has held a strong lead in the polls since the field of candidates became settled nearly two months ago.
Some black political leaders said on Saturday that there were problems at polls in New Orleans, where many people have moved around since hurricane Katrina hit in 2005.
Angie LaPlace, state elections commissioner, said she had expected many complaints because a check of voters’ addresses revealed that many people had moved.