Djokovic also draws level with tennis greats Bjorn Borg and Rod Laver on 11 Grand Slam titles.
Second seed Murray, 28, has now lost all five Australian Open finals he has played, four of them against Djokovic.
The Scot becomes only the second man – behind his former coach Ivan Lendl at the US Open – to lose five finals at the same Grand Slam since the open era began in 1968.
He was expected to head straight to the airport after the final to return to London and his wife Kim, who is due to give birth to their first child in the next two weeks.
Djokovic has now won four of the past five major tournaments, including three in a row, and will try to complete his career Grand Slam with a first French Open title in June.