Australia, touted before the tournament as favourites for gold, recovered from the disappointment of losing the lead and ultimately the semi-final against Germany in the last 15 minutes of their match on Thursday.
That close loss contrasted with Britain, who suffered a 9-2 drubbing in their semi-final against the Netherlands, and did not regain their group-stage fighting spirit when they managed to hold Australia to a 3-3 draw.
"We were just as devastated as the Brits were after their semi-final and I'm very proud of our team of how we responded today. That's a real test of character," said Mark Knowles, who already won gold in Athens in 2004 and bronze in Beijing.
"You come to the Olympics, you want to win a medal, you want gold. If you don't get to play for gold, this is the only one you can get."
Australia hold the two other main hockey titles - World Champions and Champions Trophy - and are ranked the top team in the world. They have now won bronze in four of the six Olympics since 1992, winning gold in Athens and silver in 1992.
Britain have not won an Olympic medal since 1988.
The two sides looked largely even until the 17th minute when Jamie Dwyer, five-times world player of the year, set up Simon Orchard at the top of the D and he slammed the ball home. British keeper James Fair got his hand to the ball but could not stop it.
Australia used the momentum to put the hosts under heavy pressure, missing a few good chances to extend the lead, but it was Britain who equalised from their only penalty corner of the half just six minutes before the break.
Ashley Jackson slipped the ball to Iain Lewers who put it past the keeper for a 1-1 half-time score.
But Australia came back strongly and went into the lead again when Dwyer converted a second rebound from a corner.
Nine minutes later, they ended any British hopes of bronze when Fair saved Dwyer's shot at goal but could only watch Kieran Govers whack in a volley rebound.
"If you had said seven years ago when we were awarded the Olympics and were ranked 11th in the world ... that we might come fourth, that would've felt brilliant," said Britain's coach Jason Lee.
"The truth is we've got a bad taste in our mouth from the semi-final. We had aspirations and dreams of a medal, in contrast with Australia, where everyone had expectations they would be in the big game today. I still class them as the world's top team."
Germany will defend their Olympic title against the Netherlands, whose women have already taken gold.