Djokovic, who will bid for a fourth straight title at Melbourne Park when the tournament gets underway on Monday, announced last month he had hired the six-times Grand Slam-winning German to be his head coach.
The 46-year-old Becker was a keen observer at the invitational Kooyong Classic, where Djokovic prepared for the heat of the year's first Grand Slam with a 7-5 6-1 exhibition victory over Argentine world number 42 Juan Monaco played out in steamy conditions.
"I'm really glad and honoured to have Boris in our team as my head coach," Djokovic said in a courtside interview after the sweaty contest at the Kooyong Lawn Tennis Club, a former host venue of the Australian Open until 1987.
"I sincerely hope he can bring that mental edge because he recognises the situations that one top player is facing, especially during the Grand Slams and the pressures and expectations, and the clutch moments.
"That's what we're hoping to work on and improve the most. And of course a couple of other elements of my game. I can never serve as well as he did, but I can just hope to improve."
Becker's appointment follows world number four Andy Murray's successful partnership with Ivan Lendl, who helped the Briton break through with wins at the 2012 U.S. Open and last year's Wimbledon after losses in his first four Grand Slam finals.
Roger Federer's hiring of Swede Stefan Edberg, also announced last month, means Rod Laver Arena will have no shortage of 1980s legends in the players' box in the coming weeks.
After working hard late in the season to take Serbia to the Davis Cup final, Djokovic has had a low-profile buildup, shunning the season-opening events after playing an exhibition tournament in Abu Dhabi.
But he was pleased to get back in front of an appreciative Melbourne audience, clowning around with a TV camera before his match with Monaco and raising cat-calls from the crowd when he turned a regulation shirt change into a playful strip-tease.
After a scratchy opening set, Djokovic quickly found his range, racing away in the second to close out the match in 67 minutes.
"It's great to be back, I love Australia, I love coming back here. I miss it," he said.
"You don't get (ranking) points and it doesn't really count winning or losing the match (here) but of course you want to win, especially when so many people are coming."
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- Kooyong Lawn Tennis Club