Murray, seeded second and chasing a third Grand Slam title, was drawn in the same half as Switzerland's Stan Wawrinka and Spain's Rafael Nadal.
The Scot takes on 18-year-old Zverev, a player he beat comfortably in the Hopman Cup last week. Zverev is ranked 83rd in the world.
Bedene's opponent, Johnson, is seeded 31st, seven places higher than fellow Briton Kyle Edmund's first-round opponent, Damir Dzumhur of Bosnia-Herzegovina.
Last year's men's champion and world number one Djokovic starts against Hyeon Chung of South Korea.
Swiss number two seed Roger Federer begins his quest for a fifth Australian Open victory and 18th Grand Slam title against Georgia's Nikoloz Basilashvili.
Defending women's champion Serena Williams and number five-ranked Maria Sharapova were drawn into the same section of the draw, meaning last year's finalists could meet in the quarter-finals.
Six-time champion Williams has a tough draw, starting in the opening round against Camila Giorgi of Italy, who finished 2015 at number 34 in the world and is the highest-ranked unseeded player.
Williams could also meet former world number one Caroline Wozniacki in the fourth round.
The tournament runs from 18-31 January.
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