Bolt became the only man to have retained both individual sprint golds and helped his team become the first to run under 37 seconds in the relay.
The 26-year-old Jamaican starred at the London 2012 Games as he claimed 100m, 200m and 4x100m titles. His sixth Games gold made him the most decorated Olympic sprinter of all-time.
It is the third time in the past five years he has been given the BBC honour.
“It was a great Olympics, a great year and I worked really hard,” he said.
Bolt triumphed despite hamstring and back problems that had placed his participation in doubt.
After winning the 200m title, he said: “I’m a living legend. I was fast, but I was not fit enough.”