Team GB's women's hockey team have also been named best female team at the Association of National Olympic Committees (ANOC) awards in Doha.
Britain finished second in the medal table, ahead of China for the first time, winning 17 bronzes,23 silver and 27 gold - and became the first team to win more medals after hosting the Games.
"That feat created history as we became the first nation ever to win more medals at a Games immediately after hosting, surpassing our achievement of 65 medals at London 2012," said British Olympic Association (BOA) chairman Lord Coe, who collected the award.
BOA chief executive Bill Sweeney further more :It's a fantastic achievement for both the women's hockey team and the whole of the British Olympic Association. We ever had an incredible year.
There were also awards for some of those behind some of the most memorable and inspirational moments at the Rio Games:
Best female athlete of Rio 2016
Monica Puig - women's singles tennis
Unseeded Puig had to beat top players such as Garbine Muguruza and Petra Kvitova before defeating world number two Angelique Kerber to win Puerto Rico's first Olympic gold medal - and the country's only female medallist ever.
The 23-year-old also became Latin America's first champion of the women's singles tournament.
The South African broke Michael Johnson's 400m world record, which had stood for 17 years, in a time of 43.03 seconds and is the only man ever to have won from the outside lane eight.
"Usain Bolt will be retiring soon, this could be the next star," American Johnson told BBC Sport after seeing his record smashed by the 24-year-old.
Team GB won a first Olympic hockey gold medal by beating defending champions the Netherlands in a dramatic penalty shootout.
Goalkeeper Maddie Hinch - who saved all four penalties - was trending on Twitter and the match was watched by nine million people on BBC One.
English coach Ben Ryan led Fiji's rugby sevens side to gold with a 43-7 win over Great Britain in the final - the country's first Olympic medal.
Extraordinary scenes of celebration erupted in Fiji after the final whistle - banks closed, shops shut and revellers took over the streets of Suva dancing, singing and cheering.
ANOC award for most inspirational performance.
Growing up in the infamous "City of God" in Rio, Silva took up judo at the age of seven as her parents were concerned about violence within the favela.
She became the first Brazilian judoka to become world and Olympic champion.
A team of 10 refugee athletes competed under the Olympic flag in Rio. They were selected on sporting ability - but also on personal circumstances and United Nations-verified refugee status.
The 10 competed across three sports:swimming, athletics and judo, in which Popole Misenga was the most successful team member, advancing to the round of 16 in the men's -90kg division.
They "sent a message of hope" to other displaced people across the world, according to International Olympic Committee president Thomas Bach.
As the president of the Brazilian Olympic Committee and head of the Rio Olympic Organising Committee, Nuzman was largely responsible for putting on the Games.
He was part of Brazil's first male volleyball team at the 1964 Olympics in Tokyo, Japan.
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