Douglas became the third straight American to win the top individual prize in her sport, following Carly Patterson from Athens eight years ago and Nastia Liukin at the Beijing Olympics in 2008.
She supplied four solid routines that made up part of the overall score when the United States won the team gold medal Tuesday, and she did it again Thursday.
There were 24 gymnasts in the finals and Douglas performed the best routine of all of them in the vault to get started.
She then had the third-best showing on the parallel bars before heading off to the beam, which is so often the make-or-break apparatus in gymnastics.
A fall from the beam and her hopes for a title would be over, but she recorded a score of 15.500, best of the night.
It was then just a matter of not making a major mistake in her floor exercise routine, which was judged to be fourth best among the finalists.
Douglas, 16, finished with 62.232 points. Russians Victoria Komova and Aliya Mustafina finished second and third, Komova with 61.973 points and Mustafina with 59.566.
American Alexandra Raisman had the same number of points as Mustafina, but lost the tiebreak for the bronze medal.
Douglas is the fourth American to win the Olympic gold medal. In addition to Patterson and Liukin, Mary-Lou Retton was the winner in Los Angeles 28 years ago.
Thursday's finals went on without current world champion Jordyn Wieber of the United States, who finished fourth in individual qualifying Sunday.
Rules for the competition do not allow more than two athletes from any one country in any individual final. Douglas finished second in qualifying and Raisman was third, so Wieber was forced to sit out the event.