Johnson, 33, spearheaded Australia's attack during a 5-0 Ashes sweep of England last year and then helped his team beat South Africa 2-1, picking up 59 Test wickets between August 2013 to September 2014.
This is the second time the left-arm paceman has picked up the Sir Garfield Sobers trophy, named after the former West Indian great, after winning the award in 2009.
His former captain Ponting also won the coveted prize twice in a row, in 2006 and 2007.
"Some of the greats of the game have been nominated and won this award and it's a very special honour," said Johnson.
"For me it's nice to be able to contribute to the team and do the job that I have always thought I have been able to do," he was quoted as saying in an ICC statement.
"This is something that I'll be able to look back on in time when my career is over and be exceptionally proud of."
Johnson beat the Sri Lankan duo of Kumar Sangakkara and Angelo Mathews and South Africa's AB de Villiers, who were also nominated last week.
De Villiers won the ICC one-day international cricketer of the year while England's Gary Balance was named the ICC emerging cricketer of the year.
Australian opener Aaron Finch's 156 runs off 63 balls against England in 2013 won him the ICC Twenty20 performance of the year award, while Scotland's Preston Mommsen was named the ICC Associate and Affiliate cricketer of the year.
England's wicketkeeper-batter Sarah Taylor also scooped the ICC women's one-day cricketer of the year award.
England's Richard Kettleborough of the Elite Panel of ICC Umpires won the David Shepherd Trophy for ICC Umpire of the year for the second consecutive year.
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