Selected by the Baseball Writers Association of America, the players will be inducted during a July 30 ceremony in Cooperstown, New York, according to Hall of Fame President Jeff Idelson.
The results appear to signal a softening of the voters on an issue that has long plagued the national pastime: performance-enhancing drugs
The careers of Bagwell and Rodriguez were dogged by suspicion of PED use and Raines once admitted to using cocaine during his days with the Montreal Expos.
"I think we're looking at a new wave of voters," Sports Illustrated baseball writer Tom Verducci told MLB Network.
In 2013, baseball writers balked at naming any new players to the hall,
with none of the 37 eligible players drawing enough votes for a ticket to Cooperstown.
The 2013 ballot marked the first year of eligibility for several players who have been named in the investigations of performance-enhancing drug use in the major leagues, including all-time home run champ Barry Bonds and seven-time Cy Young winner Roger Clemens.
Clemens has denied using performance-enhancing drugs, and in 2012, a federal jury acquitted him of lying to Congress during an investigation of steroid use.
Bonds, who topped Hank Aaron's home run mark in 2007, was sentenced to two years of probation and 30 days of house arrest for obstruction of justice in another federal probe. His conviction was overturned by a federal appeals court in April 2015, and federal prosecutors dropped their case against him several months later. Bonds has denied using performance-enhancing drugs.
Clemens and Bonds were on the ballot again this year -- receiving 54.1% and 53.8% of the vote, respectively. A players needs 75% of ballots cast to earn election to the hall.
Bagwell, a first baseman who played his entire career with the Houston Astros, hit .294 with 15 homers and 82 RBI in his first year, winning the 1991 National League Rookie of the Year Award.
His finished his 15-year career with a .297 average, an Astros club record of 449 home runs and eight RBI shy of Hall of Famer Joe DiMaggio at 1,529.
Bagwell was selected to four All-Star Games.
Raines came up with the Montreal Expos and played 23 years, including stints with the Chicago White Sox and New York Yankees. He played his last game in 2002, ending his career with the second-highest percentage of any player with 300 or more stolen bases.
Raines recorded 2,605 hits, 980 RBI, a .294 batting average and 808 stolen bases. He helped the Yankees win the World Series in 1996 and 1998.
Rodriguez, who appeared on the ballot for the first time this year, was a 14-time All-Star and 1999 American League MVP. He played 21 seasons for the Rangers, Marlins, Tigers, Yankees, Astros and Nationals, winning 13 Gold Glove Awards and seven Silver Slugger Awards as a catcher.
He was the 2003 NLCS MVP and helped lead the Marlins to a World Series title. Known as Pudge, Rodriguez appeared in 2,427 games as a catcher, the most in history.
Questions were raised about possible PED use by Bagwell and Rodriguez during their careers though no conclusive evidence was ever uncovered. Raines admitted using cocaine after his name came up in a 1985 cocaine scandal.
This year, there were 442 ballots -- including two blank ballots -- submitted by qualified senior members of the baseball writers associations with 10 or more consecutive years of service.
The voting baseball writers appear to be more forgiving of PED use that occurred before the implementation of a testing program in 2004.
The recent election to the Hall of Fame of former commissioner Bud Selig, who presided over the sport during the height of the PED scandal, could also explain that forgiving attitude.