Media playback is not supported on this device
He becomes the fourth Australian to lift the Sir Garfield Sobers trophy after Ricky Ponting,Mitchell Johnson and Michael Clarke.
South Africa's AB de Villiers won the ODI cricketer of the year award for the second year in a row.
Australia captain Meg Lanning was named the Women's ODI cricketer of the year.
Smith, 26, was the sixth highest run-scorer in Australia's triumphant World Cup campaign this year, with 402 runs at an average of 67, and made 1,734 in 13 Tests, at an average of 82.57.
He succeeded Clarke as skipper of the national team and led his side to a 2-0 Test series win over New Zealand last month.
Englishman Richard Kettleborough was named umpire of the year for the third time.
Sir Garfield Sobers Trophy for cricketer of the year: Steve Smith (Australia)
Test cricketer of the year: Steve Smith (Australia)
ODI cricketer of the year: AB de Villiers (South Africa)
Women's ODI cricketer of the year: Meg Lanning (Australia)
Women's T20I cricketer of the year: Stafanie Taylor (West Indies)
T20I Performance of the Year: Faf du Plessis (South Africa)
Emerging Cricketer of the Year: Josh Hazlewood (Australia)
Associate/Affiliate Cricketer of the Year: Khurram Khan (UAE)
Spirit of Cricket Award: Brendon McCullum (New Zealand)
Umpire of the Year (David Shepherd Trophy): Richard Kettleborough
Australia captain Steve Smith has been named cricketer of the year and Test cricketer of the year by the International Cricket Council.