"This is definitely something that will stay for quite some time," the 25-year-old Swiss star said. "It's not something you do overnight. It's a long, hardworking process."
Connors set his record from July 1974 to August 1977. The ATP rankings began on Aug. 23, 1973.
"It is a nice record to have," said Federer, who extended his career-high winning streak to 37 matches after beating Kristian Pless 7-6 (2), 3-6, 6-3 Monday in the first round of the Dubai Open. "I'll definitely keep it for three years. It's very hard to beat."
Federer has been ranked No. 1 since Feb. 2, 2004. He has also won six of the last seven Grand Slam titles, but hasn't played since beating Fernando Gonzalez in the Australian Open final on Jan. 28.
The only Grand Slam Federer has not won is the French Open.
Federer has 8,120 points in the yearly rankings, leading No. 2 Rafael Nadal by 3,415 points.
Since taking over the No. 1 spot, Federer is 247-15 with 34 titles in 49 tournaments. And he's never really come close to relinquishing the top ranking during that run.
"Except maybe when I played (Andy) Roddick in the 2004 Wimbledon final," Federer said Sunday. "If he had won there, he would have had the momentum, and he would have gotten close in the rankings. But I didn't lose."
Not only didn't he lose that match, Federer has also become an even better player.
"I remember when my game was still up in the air. On any given day, I could play very well. But on my off days I would be very vulnerable," Federer said. "My baseline game was OK, but not as consistent as I was hoping for. That's what I've been able to improve.
"Fitness-wise, as well, I had problems. I was always hoping not to go five sets, whereas now I don't mind it. So I've really come a long way."
Federer is fifth in the all-time list of most overall weeks at No. 1. Pete Sampras leads with 286 weeks, followed by Ivan Lendl with 270, Connors with 268 and John McEnroe with 170.
Connors won eight Grand Slam titles in his career, which lasted more than 20 years. Although he also only failed to win the French Open, Connors did win the 1976 U.S. Open on clay.
"Jimmy is one of the all-time great players," Federer said. "He played for such a long time. To stay fit through all that time with such intensity is quite remarkable."
Connors won 109 titles in his career. Federer has won 47 so far.
At last year's Dubai Open, Federer lost to Nadal in the final.