The 20-time grand slam champion had not played a competitive match since the ATP Finals in November and spoke ahead of the tournament about his concerns that he might be rusty.
There was little evidence of that as he breezed past American Johnson under the Rod Laver Arena roof, winning 6-3 6-2 6-2 in just an hour and 21 minutes.
Federer struck the ball very well but feels the real test of his form will come when he is put under pressure.
He said: "I just haven't played proper matches in many, many weeks, and a lot of guys, probably 95 per cent of the guys, are coming here with matches. So I'm not one of those guys. Now I have one. Best of five, too, which is even better.
"So I think for me really the first three rounds are key to get going, to get used to the pressure, or just to stay calm if you're down a set and a break or whatever it might be.
"This is sort of the unknown that can be a little bit scary at times. But today there was none of that because I broke early each set and was able to get on a roll, play freely after that. And also felt I had margin.
"Anything I was doing I felt like I had the game under control.
"That might not be the case in the next round, so I just think I have to be careful. Round-by-round, point-for-point mentality.
"I know other guys that are playing extremely well right now so I think it's just important to stay very calm about things right now."
The first big shock came with a 6-3 6-7 (7) 6-1 7-6 (3) loss for 13th seed Denis Shapovalov against Hungary's Marton Fucsovics.
Shapovalov cut a frustrated figure throughout and was furious with umpire Renaud Lichtenstein for giving him a code violation for throwing, but not breaking, his racket.
The young Canadian, who has been tipped to break into the top 10 this season, said: "I think I played really nervous today.
"I was in really good shape, really good conditions going into the tournament. But I just played really tight.
"Obviously I feel like my game is there to beat any of the top guys, but of course there are so many great players out there. If I'm a little bit off, if I'm a little bit nervous, anyone could beat me as well.
"It's a really disappointing one, but there's nothing to do now except learn from it."
Eighth seed Matteo Berrettini eased to a 6-3 6-1 6-3 victory over wild card Andrew Harris, while Grigor Dimitrov recovered from a set down to defeat Juan Ignacio Londero.
But 25th seed Borna Coric was a first-round casualty, losing 6-3 6-4 6-4 to American Sam Querrey.