The three were elected in their first year of eligibility after waiting the required five years after their retirement.
Right-hander Maddux, who won four consecutive Cy Young awards from 1992 and compiled a career mark of 355-227, received 97.2 percent of the 571 ballots cast.
The control specialist with a fastball that broke back over the inside corner to freeze left-handed hitters, fell shy of the record total received by former Mets pitching ace Tom Seaver, who was elected with 98.84 percent of the vote in 1992.
Lefthander Glavine, who won 305 games and was a 20-game winner five times, was named on 91.9 percent of the ballots.
Thomas, who spent most of his career with the Chicago White Sox, became the first inductee to have played most of his games as a designated hitter after blasting 521 home runs with a career batting average over .300.
The imposing, 6-foot-5 (1.96 m) slugger, nicknamed "The Big Hurt", was named on 83.7 percent of the ballots cast.
It marked the first time three players were voted into the same Cooperstown class since George Brett, Nolan Ryan and Robin Yount in 1999.
Just missing the 75 percent of the ballots cast (429)required for election was Craig Biggio of the Houston Astros, who fell two votes shy of election with 74.8 percent in the balloting.
The results were in stark contrast to last year, when no players received the required votes for induction as first-timers Barry Bonds and Roger Clemens were snubbed.
Major League Baseball home run king Bonds, a seven-time Most Valuable Player, and seven-time Cy Young winner Clemens lost ground from last year's voting, once again shunned over suspicions they had used performance enhancing drugs.
Clemens was named on 35.4 percent of ballots, and Bonds on 34.7 percent.
The inductees will be joined in this summer's July 26 induction ceremony in quaint Cooperstown in upstate New York by former managers Bobby Cox, Tony La Russa and Joe Torre.
Cox, La Russa and Torre rank third, fourth and fifth in managerial victories in Major League history, each winning more than 2,000 games, and were previously voted in by a special committee.