American Williams, a 23-times singles Grand Slam champion, and Swiss maestro Federer, who won 20 majors, had an outsized impact on the sport, both on and off the court, and their absence has been keenly felt.
International Tennis Federation (ITF) chief Haggerty hoped the Grand Slam title race between Rafa Nadal and Novak Djokovic would continue for a while longer but said the likes of US Open champion Carlos Alcaraz were already proving themselves on the big stage.
"I go back to when I was younger and would hear some of the same concerns that were raised when Pete Sampras, Andre Agassi, Jim Courier...when that generation was retiring and moving on," he told Reuters on Tuesday.
"And we've seen that the void that people thought might be there was filled with top players. I say the same thing today.
"We have had good matches on the men side with Alcaraz and Jannik Sinner. In the Australian Open we saw some of the young American players come through to the quarter-finals."
Haggerty said the women's game was also in fine fettle with Roland Garros and U.S. Open winner Iga Swiatek filling the void left by former world number one Ash Barty after her retirement.
"People were concerned with who's going to be the top woman player," Haggerty said. "And Swiatek went on a great streak of wins and showed the world she was the one.
"Tennis has some great stories and personalities as well that will continue to grace the stage and make it the important sport that it is."
