Also elected to the Class of 2010 on the eve of the Super Bowl were Russ Grimm, John Randle, Rickey Jackson, Floyd Little and Dick LeBeau.
Rice, 47, owns virtually every significant receiving record, including receptions (1,549) and yards (22,895), and has scored more touchdowns (208) than anyone.
Smith, 40, rushed for a record 18,355 yards during his 15 NFL seasons, most of them spent with the Dallas Cowboys.
“My father instilled in me hard work and appreciation for the game,” Rice, a 13-time Pro Bowler widely considered the top receiver to the play the game, told reporters.
“And I love this game. It was really everything to me. I am honored to be here, to be in front of all of the legends who made football what it is today.”
Rice played with the San Francisco 49ers from 1985-2000, before finishing his career with the Oakland Raiders (2001-04), and the Seattle Seahawks (2004)
He was not the most gifted receiver athletically but his work ethic was unparalleled.
“There is a sacrifice you have to make if you want to be the best. I respected this game. I had two great Hall of Fame quarterbacks, Joe Montana and Steve Young, a great owner Eddie DeBartolo, and a great coach. I really loved (the late) Bill Walsh.
“We went out there and we worked and we played the game the right way.”
Smith was a bruising running back despite being only 5-foot-9. He rushed for 164 touchdowns, won three Super Bowls with Dallas, and was the MVP in the Cowboys’ title-winning 30-13 triumph over Buffalo in 1994.
He often spoke of breaking Walter Payton’s all-time rushing record, which he did in 2002, but never mentioned making the Hall of Fame.
“I was so busy wanting to focus on the things I needed to do from that point on to whenever God said my career was going to be over,” he said.
“I believed in that little giant inside of me that said, ‘I can.’ Coupled with the people that I was able to play with, I felt at the end of my career all of this would be added unto me.
“This is such a special moment. This is one that you don’t think about. When you add this cake, and the icing, and the ice cream on top of that, it makes it very, very special.”
Smith began crying when he recalled a conversation with his father, an outstanding high school running back in Florida, just before the Hall of Fame results were revealed.
“He said: ‘I’m proud of you. I had the dreams of doing what you’re doing. But my mother got sick and I never did go to college. You’re living my dream.'”
The enshrinement ceremony at the Canton, Ohio, museum will be held on August 7.