Gavin Bonner's brother, Croydon, also lives in Britain.
Gavin Bonner took his place with four other heroes hailed by the society as "shining examples of great bravery in difficult situations".
He also won the personal praise of the society's secretary, Dick Wilkinson. Mr Wilkinson said: "Mr Bonner suffered injury and illness as a result of this remarkable rescue, and risked far worse.
"He was running with a friend along the Albert Embankment behind St Thomas Hospital when they heard a splash and realised a man had jumped into the water.
"Mr Bonner grabbed a life ring and threw it to the man as his friend called 999.
"But when he realised the man was making no effort to grab the life ring, Mr Bonner kicked off his running shoes and dived into the water.
"He held the man above water for 16 minutes until a fire rescue vessel arrived on the scene.
"Without doubt Mr Bonner's selfless heroism saved this man's life, and he thoroughly deserves our bronze medal award," Mr Wilkinson said.
Speaking after the presentation, Mr Bonner said his experience as a triathlete - he has competed in Iron Man events - stood him in good stead for the rescue. But he added that even so, he was ill-prepared for the ordeal he went through.
"It was very cold," he said, "ice cream headache cold!" He added: "It's a great honour to be here. I had no idea this was coming."
Craig Bonner said that his modest son informed him of the daring rescue only by text message.
He said he was delighted to attend the ceremony and every moment had made the long journey from New Zealand worthwhile.