Murray will go into the year's first grand slam having played only two competitive matches since undergoing back surgery in September.
The Scot's defeat to Florian Mayer in the second round in Doha last week, when he faded badly after a bright start, indicated it will be some time before he is back to his best.
But Becker said: "Whoever has won the US Open and has won Wimbledon can win the Australian Open.
"I saw him in Abu Dhabi and I saw him perform in Doha. The big question for him with his back surgery is how quickly can he get match fitness.
"He's the first to say he needs many more matches to get into top shape but he's been in the final three times, he knows exactly how to play well in this tournament and he loves Australia.
"And, with (coach Ivan) Lendl in his corner, I'm sure he'll be well prepared."
Two-time former Australian Open champion Becker is back at Melbourne Park for the first time in 15 years in his new role as head coach of Novak Djokovic.
The news caught the tennis world by surprise when it was announced in December, and there will be almost as much attention off the court as on it when the tournament starts on Monday.
The success of Murray's two-year partnership with Lendl appears to have inspired a number of players to turn to former greats.
As well as Djokovic and Becker, Roger Federer will team up with Stefan Edberg while former grand slam champions Goran Ivanisevic, Michael Chang and Sergei Bruguera are also new to the coaching circuit.
Djokovic is looking for an extra mental edge from having a six-time grand slam champion in his corner, and Murray will hope Becker does not have the same success against Lendl as a coach as he did as a player.
The pair met in three grand slam finals, with Becker winning all of them, although Lendl won 11 of their 21 matches overall.
Becker said: "I've been in 10 grand slam finals, I know exactly what a player feels like when he's in the later stages of a tournament.
"It's been a trend in tennis ever since the relationship between Lendl and Murray worked. It's smart because when we played in the mid-80s to late 90s it was a little bit slower but it's not that different.
"When you're 25 - in my case - I was better with a tennis racket and now I'm better with my mouth.
"I think it's a bigger media story than it is for Lendl and Edberg and Chang and myself. We've battled each other when were younger and now we have our men battling each other.
"And of course we want to win, of course we are very competitive, but I think it's about Djokovic, Murray and Nadal and some of the other players and not so much about the coaches."
Djokovic's long-time coach Marian Vajda remains part of his team but will only travel with Djokovic to a few tournaments, with Becker taking the lead role.
The Serbian has won five grand slam titles in the last three seasons and goes into the Australian Open on a run of 24 straight wins but being usurped by Rafael Nadal as world number one clearly hurt.
Becker said: "I was honoured that a player like Djokovic would call me for help. We've had a wonderful couple of weeks already and I'm going to do the best I can to make him even better.
"He's not happy with six grand slams even though that's an incredible record by itself. He wants to win more."
The draw was kind to Djokovic, who has won the title for the last three years and will open against Slovakia's Lukas Lacko.
By far the highlight was the pairing of top seed Nadal with great Australian hope Bernard Tomic in a loaded top half of the draw.
Also in there is fourth seed Murray, who at least should have a gentle opening against Japan's Go Soeda but is seeded to meet Federer in the quarter-finals and Nadal in the semis.
British number one Laura Robson, who is battling to get over a wrist problem, was given a tough opening against 18th seed Kirsten Flipkens.
World number one Serena Williams plays Australian wild card Ashleigh Barty while defending champion Victoria Azarenka meets Johanna Larsson of Sweden and third seed Maria Sharapova takes on America's Bethanie Mattek-Sands.