With top seed Rafael Nadal and fourth seed Andy Murray both victorious on Monday, Djokovic and Federer needed to give an early display of their title credentials.
Djokovic, the form player of 2011, was arguably the most impressive, with his 6-4 6-1 6-1 demolition of Jeremy Chardy coming in an hour and 20 minutes.
Federer was also an impressive straight-sets winner, beating Mikhail Kukushkin 7-6 (7/2) 6-4 6-2.
It was Djokovic’s first match since his 43-game unbeaten run was halted by Federer in the French Open semi-finals, and he was pleased with how quickly he got back in the groove.
“That was my first official match on grass so it took some time to get adjusted,” he said.
“When my streak ended in Paris, it was kind of a relief as well, because it’s been a very successful five, six months, but it’s also been long and exhausting.”
Federer, the six-times champion, is bidding to equal Pete Sampras’s open era record of seven Wimbledon titles, while Kukushkin was a grass-court rookie and after showing early promise, he began to fade.
Andy Roddick began another bid for Wimbledon glory with a 6-4 7-6 (8/6) 6-3 victory over qualifier Andreas Beck on Court One.
Germany’s Tobias Kamke set up a second-round clash with fourth seed Murray by beating Slovenian Blaz Kavcic 6-3 7-6 (7/4) 5-7 6-1.
As is now customary, Murray is the only British male standing going into the second round, with Daniel Evans, James Ward and Dan Cox all going out.
Serena Williams broke down in tears after putting a year-long nightmare behind her to make a successful start to the defence of her Wimbledon crown.
Williams, playing only her second tournament since recovering from a serious foot injury and blood clots on her lungs, finished strongly against world number 61 Aravane Rezai to win 6-3 3-6 6-1.
The American said last week the blood clots had left her “on her deathbed” and she was overcome with emotion after her win.
“I’m not a crier. I just expected to walk off,” said Williams, who will play Romania’s Simona Halep in the second round.
Caroline Wozniacki took just 59 minutes to power past Arantxa Parra Santonja, 6-2 6-1.
The Dane is under pressure to perform well here to justify her position atop the rankings despite not having won a grand slam in her short career.
Virginie Razzano set up a second-round clash with Wozniacki after winning for the first time since her husband and coach Stephane Vidal died of a brain tumour, beating Sania Mirza of India 7-6 (7-4) 2-6 6-3.
The Frenchwoman said. “I had some problems at the start, but I said to myself, ‘Now you must be aggressive. You are here to play for you and for Stephane’.”