Smith was the only player picked, with Gary Carter falling just short.
A 13-time Gold Glove winner while with the St. Louis Cardinals and San Diego Padres, Smith was chosen on 91.7 percent of the ballots.
The Wizard of Oz became the 37th player picked in his first year of eligibility.
Smith was selected on 433 of 472 ballots. To be elected, players had to be listed on at least 75 percent of the ballots of 10-year members of the Baseball Writers' Association of America.
Carter got 343 votes (72.7 percent) and fell 11 shy of election. The former catcher's totals have dramatically improved over the years, going from 34 percent in 1999 to nearly 49.7 percent in 2000 to 65 percent last year.
Luis Tiant (18 percent) fell of the ballot in his 15th and final year of eligibility. Ron Guidry, Dave Stewart and Frank Viola were among the players who failed to receive the required 5 percent to remain on the ballot.
Smith, 47, was a 15-time All-Star in his career. He will become the 254th person inducted into the Hall in ceremonies at Cooperstown, N.Y., on July 28.
Smith won 13 NL Gold Gloves all in a row from 1980-92 set shortstop records for most assists (8,375) and double plays (1,590) and entertained fans with a backflip when he ran out to shortstop at the start of games. The Cardinals retired No. 1 in his honor.
"I don't think anybody ever played the position any better than he played it," former Cardinals manager Whiey Herzog said Monday.
"Was he the best?" Herzog said. "He made more diving plays than I've ever seen. I don't see how it was possible to play it any better than Ozzie played it."
Smith spent 19 seasons in the major leagues, breaking in with San Diego in 1978. Smith played four years with the Padres, then finished with 15 years in St. Louis.
Smith was not known for his offense. He batted just .262 in his career with 2,460 hits, 28 homers and 793 RBIs.
But Smith could deliver in the clutch. A switch-hitter, the first left-handed homer of his career came in the bottom of the ninth inning of Game 5 of the 1985 NL championship series, lifting the Cardinals over Los Angeles.
The Cardinals went on to win the series in six games, and Smith was voted MVP of the NLCS.
"It's been a lot of fun," Smith said during his final season. "People have been nice to me. I've been shown a lot of respect and a lot of admiration for what I've tried to bring to the game, and that's all you can ask."
Carter, an 11-time All-Star, was on the ballot for the fifth time. He was picked on 42.3 percent of the ballots in his first appearance in 1998. His percentage dropped to 33.8 the following year, then increased to 49.7 in 2000 and 64.9 in 2001.
Carter hit 324 homers with 1,225 RBIs. His 298 homers as a catcher are the sixth-most.
Rice, on the ballot for the eighth time, was fourth in last year's voting at 57.9 percent. The eight-time All-Star and 1978 AL MVP had a .298 career average with 382 homers and 1,451 RBIs.
Sutter and Gossage were bidding to join Hoyt Wilhelm and Rollie Fingers as the only relievers in the Hall.
Alan Trammell got 16 percent in his first year of eligibility.
©MMII, The Associated Press. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed