Serbia's Djokovic, 35, lost the first set after some superb serving from Kyrgios, but ended up winning 4-6 6-3 6-4 7-6 (7-3) on Centre Court.
It is Djokovic's seventh SW19 men's title and only Roger Federer has more.
Victory also moved him one behind Rafael Nadal's record 22 men's majors.
Top seed Djokovic made a slower start than his 27-year-old opponent, who initially seemed nerveless in his first Grand Slam singles final.
But the Serb did not lose belief as he showed all of his experience and nous to turn the match around.