Bagwell (381 votes) received 86.2 percent of the vote, one year removed from falling just 15 votes shy of the 75 percent needed to gain entry into the exclusive club.
Raines (380) garnered 86 percent on his final year on the ballot and Rodriguez (336) had 76 percent of the vote to become the second catcher in the history of the voting to be elected on his first year on the ballot.
The trio will be honored along with former commissioner Bud Selig and executive John Schuerholz as well as the late Bill King and Claire Smith as part of the Hall's Induction Weekend on July 28-31. King is the Ford C. Frick Award winner for broadcasting and Smith is the J.G. Taylor Spink Award winner for writing.
Players must receive 75 percent of the vote from eligible Baseball Writers' Association of America members to be elected. Voters can list 10 players, who remain eligible for one 10-year window.
Relief pitcher Trevor Hoffman (327, 74 percent) fell five votes shy of gaining entry on his second year on the ballot. Outfielder Vladimir Guerrero received 317 votes (71.7 percent) as a first-year candidate.
Bagwell received Rookie of the Year and Most Valuable Player honors during his 15-year career with the Houston Astros. Bagwell, who belted 449 homers, made four All-Star teams and won three Silver Slugger Awards.
Raines was a seven-time All-Star with the Montreal Expos during the 1980s and saw his career span 23 years while playing with the Chicago White Sox, New York Yankees, Oakland Athletics, the then-Florida Marlins and Baltimore Orioles. He ranks fifth in history behind Rickey Henderson, Lou Brock, Billy Hamilton and Ty Cobb with 808 stolen bases, and his 84.7 percent success rate is the best among players with at least 400 attempts.
Rodriguez was the American League MVP in 1999 and accrued 14 All-Star selections to establish himself as one of the best catchers of his generation. He batted .296 (2,844 hits) with 311 homers and 1,332 RBIs in 21 seasons with six teams.