Smith also scored four centuries and 1,249 runs in 25 one-day internationals from Sept. 18, 2014 to Sept. 13, 2015, notching up the winning runs as Australia stormed to a fifth World Cup triumph.
"I'm obviously completely surprised by it, very humbled," said Smith, who was also part of the team that lost the Ashes to England during the voting period.
"You don't think about these accolades, you just want to go out there and do the best you can for the team and try and win as many games as possible.
"My favourite moment would have to be winning the World Cup, playing against New Zealand at a packed house at the MCG. It was an amazing feeling to be able to hit those winning runs."
The Australian also scooped the ICC Test Cricketer of the Year award while South Africa batsman AB de Villiers was rated the best player in the one-day game, winning the award for the second successive year.
De Villiers, South Africa's captain in the ODI format, also won the award in 2010.
The 31-year-old's brilliant quickfire batting lit up the World Cup, not least his unbeaten 162 against West Indies in Sydney, and he racked up 1,265 runs in total at an average of nearly 80 an innings over the relevent period.
His team mate Faf du Plessis won the award for best Twenty20 performance of 2015 for his 56-ball innings of 119 against West Indies in January, the third highest score of all time in T20 internationals.
Australian paceman Josh Hazlewood was named best emerging player, while the Spirit of Cricket Award went to New Zealand captain Brendon McCullum, who made a virtue of his team's sportsmanship as he led them to the final of the World Cup.
McCullum said on Tuesday that he would be retiring from international cricket after the two-test series against Australia in New Zealand in February.
Australia captain Meg Lanning was the women's One Day International Cricketer of the Year, while her West Indies counterpart Stafanie Taylor won the women's Twenty20 award.
Khurram Khan of the United Arab Emirates was named Associate and Affiliate Cricketer of the Year, while England's Richard Kettleborough was named best umpire for a third year in a row.
(Reporting by Nick Mulvenney, editing by Sudipto Ganguly)
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