With a classic one-handed backhand, Henin won seven Grand Slam singles titles and an Olympic gold medal and helped Belgium win its first Fed Cup championship. She spent 117 weeks ranked No. 1 and finished the 2003, 2006 and 2007 seasons in the top spot.
Henin won four French Opens, two U.S. Opens and one Australian Open despite a small frame in a game increasingly dominated by power.
''Not a lot of people really believed I could reach my goal because my dream was to become the best player in the world,'' she said on a conference call Tuesday. ''It became my goal. A lot of people thought I was a little bit crazy. But strongly, deeply I never really doubted about the fact that I could make it.''
The enigmatic Safin earned two major titles - at the 2000 U.S. Open and 2005 Australian Open - and briefly reached No. 1. He is the first Russian elected to the Hall.
''Very difficult to come out of the country. No money,'' he said. ''To come out of the country and start to play on the world level, I think it's a really big achievement.''
Also in the Hall's Class of 2016: Yvon Petra and Margaret Scriven were posthumously elected in the master player category.
At about 5-foot-6 and 125 pounds, Henin was often smaller than her opponents, but that never mattered. She covered the court as well as anyone, used that backhand John McEnroe once called the prettiest shot in the game, and mixed in rushes to the net - punctuating winners with ''Allez!'' and a fist pump. She is also the first Belgian elected to the Hall.
Henin once used the phrase ''Impossible is nothing,'' and one of her sponsors turned that into a marketing slogan. It reflected her on-court philosophy, highlighted by a victory over Jennifer Capriati in the 2003 U.S. Open semifinals in which she was two points from defeat 10 times. Henin needed IV fluids after that match, which ended after midnight, but won the final the next day.
Henin also was the first woman to beat both Venus and Serena Williams en route to a major title.
''I always thought that I could use my qualities: I was quick; I could anticipate the game,'' she said. ''Physically at the end I worked very hard and I could compensate. I wasn't as powerful, but I could use other parts of my game.''
Safin was one of the most unpredictable and outspoken stars of tennis. He burst onto the scene by beating Pete Sampras in the final of the 2000 U.S. Open, and predictions of many more major titles soon followed.
But while Safin did add a second Grand Slam trophy, his career became as well known for his smashed rackets and other antics - whether it was celebrating a terrific shot at the French Open by grabbing his white shorts and tugging them down to his thighs or complaining about the high price and low quality of the food in the players' restaurant at Wimbledon.
''Obviously back then I would love to win much more tournaments, more Grand Slams, more things in my career,'' Safin said. ''But unfortunately I had a lot of injuries also. Sometimes probably I wasn't well prepared for what I was going through. I had lack of experience and not the right decisions were taken.''
France's Petra won Wimbledon in 1946, following five years as a prisoner of war in Germany, according to the Hall. Petra died in 1984.
Britain's Scriven won the French Championships - the precursor of the French Open - in 1933 and 1934. She was the first left-hander to win a Grand Slam title. She died in 2001.