Left-arm quick Johnson (168 votes) came from behind to run down test and one-day captain Michael Clarke (156) during the recently completed home Ashes series.
"I was very surprised, very emotional," Johnson said.
"I guess the emotions probably flowed from what's happened in the past 12 months and even before that.
"I guess all the hard work and the blood, sweat and tears that you go through and the ups and downs of a professional sportsman, all just came out tonight and I didn't expect to win."
Injury and form issues cast clouds over 32-year-old Johnson's international career during 2003.
He missed the Ashes series in England, but performed well in the one-day series there.
He made a spectacular test comeback in the home series in which he claimed 37 wickets at 13.97 and was a pivotal figure in Australia regaining the urn.
"It has been an amazing journey coming back from injury, having a lot of doubters out there," Johnson said.
"But I just knew in my own heart that if I had that opportunity that I could make the most of it."
He polled votes in three tests of the Ashes series in Australia, while Clarke collected votes in just one.
Clarke played seven more tests than Johnson in the voting period from February 1, 2013 to January 20, 2014, but the speedster notched eight more ODI appearances than his captain.
Across the three formats, Johnson collected more wickets than any other Australian, while Clarke had the second-highest run-scoring aggregate behind Shane Watson.
Clarke, who had won the medal the past two years, was denied a record fifth triumph.
"He (Johnson) well and truly deserves the Allan Border Medal," Clarke said.
Emerging Tasmania allrounder James Faulkner (121) underlined his growing presence in Australian cricket by finishing third after placing second earlier in the evening in both the Twenty20 and one-day awards.
All-rounder Watson (119) finished fourth in the voting, with batsman George Bailey and Steve Smith (both 114) equal fifth.
Earlier, Clarke won the test player of the year for a record fourth time.
"I don't think I've performed anywhere near as well, especially throughout the last series, as I would have liked," Clarke said.
George Bailey was named one-day player of the year a few hours after his omission from the test squad to tour South Africa was announced.
"To be honest I was more hoping than expecting to be on the tour," Bailey said.
"I think I said at the start of the series that at 31, you probably only get one crack at it, but I'm hoping now to prove myself wrong."
Aaron Finch collected the Twenty20 player of the year award.
Victorian opener Meg Lanning won the Belinda Clark Medal for the premier female player of the year, Victorian Cameron White was named domestic player of the year and Tasmanian batsman Jordan Silk was presented with the Bradman young player of the year award.
