Henin, 34, the first Belgian elected to the shrine, said standing in the spotlight was difficult for her but very much appreciated as the culmination of a dream that began at age six.
"Being the centre of the attention is not always the best for me," she told reporters. "Today is also quite emotional, not only get this honour, but also need to remember how hard was the way, but how beautiful was the way from the little girl of six years old that was not that big.
"Being part of the history of the game, it's much more than I could expect for as a little girl. I'm really proud, happy."
Safin burst to prominence with a stunning straight-sets rout of Pete Sampras in the 2000 U.S. Open final and added the 2005 Australian Open crown over Lleyton Hewitt in addition to helping Russia win two Davis Cup championships.
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The big Russian, known for taking his frustrations out on his rackets and tennis balls, said he felt like a kid in Disneyland in visiting the Hall of Fame museum.
"This is an amazing place. You feel the power, the energy. You can see what kind of people are living here before. You have a museum, a beautiful place," said Safin, 36, who turned to politics after retiring from tennis, winning election to Russia's parliament, the Duma, in 2011.
"We had ups and downs, we cried, we broke the rackets, we shouted some words, we throwed the balls out of the court, we insulted the referees, only sometimes," he continued to laughter, bringing back memories of his fiery on-court temperament.
"I'm just so pleased to be part of it. It's a huge honour to be inducted and be part of the history."
Mauresmo, an Australian and Wimbledon champion and first French woman to reach world number one, said joining the Hall of Fame community was a thrill.
"You feel part of a special family that have achieved special things," she said. "It's such a great honour, privilege."
Henin, remembered for her all-round game and devastating one-handed backhand, said her fate was sealed at an early age.
"At 10 years old I went to the French Open. It was the final between Steffi (Graf) and Monica (Seles)," recalled Henin. "I said to my mum, 'One day I will be on this court and I will win.'
"I was getting to my bedroom, I was jumping like I was winning the French Open. For me, it was clear I was going to do that. French Open and number one," she added. "At 21 it became real."
(Reporting by Larry Fine in New York; Editing by Andrew Both)
