Keeper Boubacar Barry saved a penalty then scored the winning spot-kick, the game having finished goalless after extra-time in Bata, Equatorial Guinea.
Barry seemed to be suffering from cramp during a shootout in which five penalties were missed.
But the 35-year-old’s heroics gave the Ivorians their second title, in a repeat of the 1992 final.
Twenty-three years ago, Ivory Coast lifted their first trophy when they beat Ghana 11-10 on penalties after a goalless draw.
Ivory Coast missed their first two kicks – Manchester City’s new signing Wilfried Bony hit the crossbar and substitute Junior Tallo dragged wide with his first touch of the game – but Afriyie Acquah and Frank Acheampong failed with their efforts for Ghana.
After every outfield player had taken his turn, Barry brilliantly saved Ghana keeper Brimah Razak’s effort.
Having annoyed some of the Ghana players when he delayed their kicks because of cramp, Barry slotted home straight before being mobbed by his team-mates.
Frenchman Herve Renard became the first coach to win two Africa Cup of Nations with different countries, following Zambia’s success in 2012.
Ghana had the better of the chances in the match and twice hit the woodwork.
Christian Atsu was unlucky to see a superb 25-yard shot come back off the keeper’s left-hand post, while Andre Ayew struck the outside of the other upright from a tight angle.
But there there was a sense of inevitability throughout the match that it would go the distance as neither team appeared to be prepared to take the risks that might bring a victory.
The big names – Ivory Coast’s Yaya Toure and Bony, and Ghana’s Ayew and Asamoah Gyan – failed to have a decisive influence on the game, which never really flowed.
This was the sixth time in the last 12 tournaments that the final went to penalties, two of which had been lost by Ivory Coast.