The club was established as an expansion team of the Double-A Southern League in 1978, in which it competed through 1984. While at that class level, Nashville was affiliated with the Cincinnati Reds (1978–79) and New York Yankees (1980–84). The franchise moved to the Triple-A American Association in 1985 and then to the Triple-A Pacific Coast League in 1998. At this class level, the team has been affiliated with the Detroit Tigers (1985–86), Cincinnati Reds (1987–92), Chicago White Sox (1993–97), and Pittsburgh Pirates (1998–2004). Since 2005, Nashville has been the Triple-A farm team of the Milwaukee Brewers.

Players Steve Balboni, Brian Dayett, and Magglio Ordóñez have each won minor league Most Valuable Player awards. Ordóñez also won the American Association Rookie of the Year award in 1997. League Pitcher of the Year honors have been awarded to Bruce Berenyi, Geoff Combe, Andy McGaffigan, Jamie Werly, Stefan Wever, Chris Hammond, Scott Ruffcorn, Jeff Abbott, and R. A. Dickey.

Forty-nine of the team's players have distinguished themselves by winning a Major League Baseball award or being named to a major league All-Star team. Barry Larkin, Don Mattingly, and Willie McGee have each won Most Valuable Player (MVP) Awards. Doug Drabek is the only former Sounds player to win a Cy Young Award. Jason Bay, Ryan Braun, and Chris Sabo have won Rookie of the Year Awards. Bob Melvin and Buck Showalter each won a Manager of the Year Award. Keith Foulke, Trevor Hoffman, and Jeff Montgomery have won the Rolaids Relief Man of the Year Award. Hoffman, Larkin, and Mattingly have won a Lou Gehrig Memorial Award. Larkin also won a Roberto Clemente Award. Prince Fielder and Aramis Ramírez have won a Hank Aaron Award. José Rijo is the only former Sounds player to win a World Series MVP Award. Five alumni have won a Rawlings Gold Glove Award, and eight have won a Silver Slugger Award. Forty-seven alumni have been named to Major League Baseball All-Star Game teams.