The left-arm quick took the prestigious Sir Garfield Sobers Trophy ahead of South Africa's AB De Villiers and Sri Lanka duo Angelo Mathews and Kumar Sangakkara.
Johnson enjoyed quite the year after storming back onto the international stage by leading Australia to a 5-0 Ashes series whitewash against England in 2013-14.
He becomes just the second player to win the award twice, alongside former Australia captain Ricky Ponting, after his previous success in 2009.
"Some of the greats of the game have been nominated and won this award and it's a very special honour," Johnson said.
"I'm very proud to be nominated and compared to these types of players.
"Aggressive fast bowlers are something you'd have seen back in the day with the likes of [Dennis] Lillee and [Jeff] Thomson.
"For me, it's nice to be able to contribute to the team and do the job that I've always thought I've been able to do.
"I suppose it comes down to the attitude I've got, the belief and the confidence. I'm very happy with where I am at the moment and I want to keep getting better as a cricketer.
"This is something that I'll be able to look back on in time when my career is over and be exceptionally proud of.
"I want to thank everyone for their support, especially my team-mates, support staff and my family for everything they've done for me. I wouldn't be sitting here today without them."
While Johnson was also named the ICC Test Cricketer of the Year, De Villiers took the one-day international award and England batsman Gary Ballance was named Emerging Cricketer of the Year.
England's Sarah Taylor was named the Women's ODI Cricketer of the Year, while Meg Lanning was the Twenty20 International Women's Cricketer of the Year.