Propelled by his father Omar's legacy and a pro-US trade agenda, Martin Torrijos, an opposition centrist, gained 46% of the vote on Sunday.
His closest challenger, former president Guillermo Endara, trailed with 29%.
Electoral officials telephoned Torrijos on live national television and told the 40-year-old construction magnate that he would be president for the next five years.
"I accept this responsibility and hope to make my country proud," Torrijos said as hundreds of supporters cheered, waved flags and danced to salsa music.
In an election that often seemed more about Panama's violent past than its stable present, Torrijos campaigned heavily on the popularity of his late father.
Torrijos senior remains beloved for negotiating the 1977 treaty that bound Washington to hand over control of the Panama Canal in 1999.
One round election
The one-round vote was the first presidential election since Panama took over the canal. Only a few minor irregularities were reported, and officials said turnout was heavy.
"I hope Martin will be just like his daddy," said Olivia Herrera, a 70-year-old secretary, as she voted. "The Torrijos family is honest, humble and they care about the poor."
The anticipated canal expansion
could be worth up to $5 billion
Many voters wore buttons bearing Omar's image, and campaign posters showed the late leader puffing on a cigar with a modern-day image of Martin superimposed in the background.
In a twist common in Panama's politics, where a few families control most of the power, Torrijos was set to replace outgoing President Mireya Moscoso - whose late husband was ousted in a coup by his father in 1968.
Moscoso was barred by law from seeking another term. The ruling party candidate, Jose Miguel Aleman, finished third.
One of six children that Omar Torrijos father with four women, Martin Torrijos portrayed himself as a self-made man who was mostly raised by his grandparents and worked at McDonald's while studying in the US.
However, political analysts say the Torrijos name made the difference in an election featuring candidates with similar market-friendly agendas. Omar Torrijos died in 1981 in a mysterious plane crash that ended his rule.
International observers said the election was relatively clean, highlighting the progress of Panama's democracy since US troops invaded in December 1989 to remove former strongman
Noriega is in a Florida prison serving a 30-year sentence on drug-trafficking charges.
Torrijos will also preside over a canal expansion that could cost $5 billion or more if it gets the anticipated go-ahead later this year from an independent panel.