Thousands of people watched a spectacular fireworks display as well as performances by hundreds of dancers and musicians.
The competition will involve more than 5,000 athletes from 42 countries.
Around 20,000 police officers will be on duty to ensure that the Games run smoothly, amid concern about the level of violence and crime in Rio.
The official opening of the games was heralded by the arrival of the Pan American torch and a parade of the more than 5,000 athletes from across the Americas.
However the tight security meant that many fans could not get to the stadium in time.
Brazil has not hosted an event of this size since the 1950 World Cup.
That was one of the country's greatest moments of sporting anguish, when the Brazilian team lost to underdogs Uruguay in the final.
Rio is hoping for better memories from this event, which is being staged in the refurbished Maracana Stadium.
It is thought up to $2bn (£1bn) have been invested to make the Games a success, several times more than was first planned.
The authorities here hope if all goes well, it will boost their chances of securing the 2014 World Cup and the 2016 Olympics.
But this has its sceptics even within Brazil, says the BBC's Gary Duffy in Rio.
There were reports of a last-minute rush to complete work, but most venues now seem to be ready.
Security will also be a concern here, amid high levels of crime and violence in Rio, our correspondent says.
The latest casualty was a 16-year-old boy, killed by a stray bullet in a suburb of the city as he prepared breakfast in his own home.
The deployment of 20,000 police officers is aimed at ensuring that everything runs smoothly.
But some recent high-profile operations meant to target drug dealers in the city's favelas, or shanty towns, have been criticised by human rights organisations.
In one day alone, 19 people died.
But the authorities deny any link between the recent escalation in police action and the Games.
The Pan-American Games are due to run to the end of July, with the athletes competing in almost 40 different sports.
Güncelleme Tarihi: 14 Temmuz 2007, 07:40