Johnson (168 votes) came from behind to run down Clarke (156) during the recently completed home Ashes series.
It was 32-year-old Johnson's first Allan Border Medal win, while Clark, who had won it the past two years, was denied a record fifth triumph.
After missing out on the Ashes series in England, Johnson made a spectacular comeback in the home series and was a pivotal figure in Australia regaining the urn.
He polled votes in three Tests of the series, in which he claimed 37 wickets at 13.97, while Clarke collected votes in just one.
Clarke played seven more Tests than 32-year-old Johnson, 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 runscoring aggregate behind Shane Watson.
"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."
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.
Allrounder 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 then year for a record fourth time, Bailey was named one-day player of the year and 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.
AWARD WINNERS FROM THE ALLAN BORDER MEDAL:
ALLAN BORDER MEDAL: MITCHELL JOHNSON
* TEST PLAYER OF THE YEAR: MICHAEL CLARKE
* ONE-DAY PLAYER OF THE YEAR: GEORGE BAILEY
* TWENTY20 PLAYER OF THE YEAR: AARON FINCH
* BELINDA CLARK MEDAL: MEG LANNING
* DOMESTIC PLAYER OF THE YEAR: CAMERON WHITE (VICTORIA)
* BRADMAN YOUNG PLAYER OF THE YEAR: JORDAN SILK (TASMANIA)