Maddux was named on 97.2 percent of the ballots and Glavine received 91.9 percent in the results of voting announced Wednesday in Cooperstown, New York.
Also elected was former Chicago White slugger Frank Thomas, the first primary designated hitter to make it into the Hall of Fame. His name appeared on 83.7 percent of the 579 ballots.
Longtime Houston Astros infielder Craig Biggio just missed election at 74.8 percent. Candidates must receive a minimum 75 percent to be voted in.
Former Los Angeles Dodgers and New York Mets catcher Mike Piazza fell short at 62.2 percent and longtime Detroit Tigers and Minnesota Twins pitcher Jack Morris failed again, getting 61.5 percent.
Barry Bonds (34.7 percent) and Roger Clemens (35.4), whose candidacies are tainted by allegations of performance-enhancing drugs usage, lost support compared with last year.
Maddux, Glavine and Thomas will be joined in the induction ceremony by Cox and former managers Tony La Russa and Joe Torre, who were elected by the Hall of Fame's Expansion Era committee last month.
"It's exciting for me to go in with my teammate," Maddux said.
Maddux, 47, ranks eighth in baseball history in wins (355), 10th in strikeouts (3,371) and fourth in games started (740). An eight-time All-Star, Maddux compiled a career 355-227 record with a 3.16 ERA.
Glavine, 47, was Maddux's teammate with the Braves from 1993-2002. He pitched in the majors 22 years, 17 of them with the Braves, five with the New York Mets. A 10-time All-Star and two-time Cy Young Award winner, Glavine finished 305-203 with a 3.54 ERA in 682 career starts.
Thomas, 45, won back-to-back American League MVP awards with the Chicago White Sox in 1993 and '94. He placed in the top three in MVP voting five times overall. "The Big Hurt" finished his 19-year career with 2,468 hits, including 521 home runs. He drove in 1,704 runs, scored 1,494 and had more walks (1,667) than strikeouts (1,397).
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The Los Angeles Dodgers and manager Don Mattingly reached an agreement on a three-year contract, general manager Ned Colletti confirmed Wednesday.
"I think he's done a great job here," Colletti said of Mattingly at a news conference at Dodger Stadium.
"The last three years in the organization have been historic in a lot of different ways," Colletti said. "We kept the baseball team steady and the credit goes to a lot of people, including the man who runs the dugout and the leader of the guys. This is well deserved. He gets better and better."
Mattingly, 52, already was under contract for the 2014 season. The new deal takes him through the 2016 season.
Mattingly faced an uncertain future last season, and rumors swirled that he was on the verge of getting fired before the team went on a 42-8 run and ultimately won the National League West title by 11 games.
The Dodgers advanced to the NL Championship Series, which kicked in a clause in Mattingly's contract, guaranteeing his $1.4 million contract for 2014.
Following the season-ending loss to the St. Louis Cardinals in the NLCS, Mattingly said he was uncertain the Dodgers wanted him to return.
The Dodgers' 92-70 record last season improved Mattingly's three-year record in Los Angeles to 260-225.
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Highly coveted Japanese pitcher Masahiro Tanaka is set to meet with the Chicago Cubs and the Chicago White Sox this week, according to a report.
Sportsnet reported that the right-hander will be in Chicago while accompanied by agent Casey Close, who is traveling with Tanaka on a tour of major-league cities.
The Cubs and White Sox had no comment on the report.
Suitors are lining up for a shot at landing the 25-year-old, who posted a 24-0 record with a 1.27 ERA in 212 innings last season for the Rakuten Golden Eagles in Japan. Other teams mentioned as possible destinations include the Los Angeles Dodgers, Texas Rangers, Seattle Mariners and Arizona Diamondbacks.
Dodgers general manager Ned Colletti tweeted Wednesday that he is in the "feeling out process" with Tanaka's agent.
The deadline is Jan. 24 for teams to pay a $20 million posting fee to the Golden Eagles. Tanaka is likely to command a major-league contract that will exceed $100 million.