The Swiss sixth seed cruised past Australian wildcard James Duckworth 6-4, 6-4, 6-2 in one hour 46 minutes on Rod Laver Arena.
The record 17-time Grand Slam title winner teamed up with former world number one and six-time major champion Edberg last month.
Roger Federer. Pic/ AFP
Federer coped well with heatwave temperatures hovering around 40 Celsius (104 Fahrenheit) to set up a second-round match against either Czech Radek Stepanek or Slovenia's Blaz Kavcic.
The Swiss great broke Duckworth's service four times and only faced one break point in his 14 service games. He hit 30 winners with 17 unforced errors to ease through to the next round.
"It's great fun to be playing in front of him (Edberg) and it's been a dream come true for me," Federer said.
"I used to watch his matches and get inspired to play this great game so to have him in my corner through the year and this tournament is very special and I can't be thankful enough."
Federer said the heat made for quick conditions on court and that he had difficulty finding his rhythm and getting into rallies.
"I'm feeling okay, it's not crazy so I'm happy with how I am feeling this way right now," Federer said of coping with the extreme heat.
Federer is bidding to become only the second man after Australia's Roy Emerson to win five Australian Opens. He has never lost in the first round in 15 appearances.
He came into the major tournament having lost to old Australian rival Lleyton Hewitt in the final of the Brisbane International over a week ago.