Djokovic took the match in London's sunshine 6-2 6-2 7-6 in two hours and 18 minutes.
For the Serbian it is also a 13 major, whilst Anderson - also a finalist at last year's US Open - was aiming to win a maiden slam.
Defensive Djokovic was comfortably the more consistent player, making only 13 unforced errors compared to Anderson's 26.
Prior to his first Wimbledon final, Anderson came through an epic semi-final clash - beating American John Isner over five sets in six hours thirty-six minutes.
Djokovic's first slam success since the 2016 French Open ensures he will be back in the ATP's world top 10.