A total of 425 ballots were cast, with 319 needed for election.
Players will be inducted July 21 in Cooperstown, New York, at the National Baseball Hall of Fame & Museum.
Halladay and Martinez each received 85.4 percent of the vote, while Mussina drew 76.4 percent of the vote.
Rivera, 49, who compiled 652 saves during the regular season and 42 more in the postseason, was elected in his first year of eligibility. He had an 82-60 record and a 2.21 ERA during a 19-year career that ended in 2013. In the postseason, Rivera was nearly untouchable with a 0.70 ERA.
Halladay, who was killed in an airplane crash off the west coast of Florida in November 2017, won 203 games during his 16-season career. This was also his first year on the Hall of Fame ballot.
In 2010, he became the second pitcher in major league history to throw a postseason no-hitter, blanking the Cincinnati Reds to join Don Larsen, who threw a perfect game in Game 5 of the 1956 World Series.
Martinez, 56, becomes the first player to be inducted into the Hall of Fame who was primarily a designated hitter. Martinez, who played his entire 18-year career with the Seattle Mariners, was elected in his 10th and final year of eligibility.
Mussina, 50, was elected in his sixth year of eligibility. He won 270 games during an 18-year career he split between the Baltimore Orioles and New York Yankees.
Mussina won 11 or more games in every season except his rookie year, 1991.