Nadel grew up in Brooklyn, New York, as a fan of the Brooklyn Dodgers and decided at a young age that he wanted to be a sports broadcaster. He developed his skills at Brown University, announcing hockey and football games on radio station WBRU. He had minor league hockey play-by-play stints in Muskegon, Oklahoma City, and Dallas, and was also the radio voice of the Dallas Diamonds of the Women's Professional Basketball League. The Rangers hired Nadel in 1979, and he called games on television and radio in his first three seasons. Beginning in 1982, he began a 13-year run with Mark Holtz as the radio team on WBAP, returning to the television booth for one year in 1984. Nadel became the team's lead radio voice when Holtz moved to television in 1995. Since becoming the primary play-by-play voice for the Rangers, Nadel has worked alongside Brad Sham, Vince Cotroneo, and Victor Rojas. In May 2006, Nadel announced that he had signed a "lifetime contract" with the Rangers, allowing him to continue on their broadcast team until he chooses to retire. He later said that he hopes to outlive his contract. Beginning in 2009, he was partnered with longtime ESPN and former Dallas Mavericks and San Antonio Spurs announcer Dave Barnett, who also did Rangers games on television with Brad Sham in the late 80s and early 90s. After Barnett moved to television, former MLB pitcher Steve Busby was Nadel's partner. Since July 2012 after Busby replaced Barnett on television, Nadel has been joined by Matt Hicks in the radio booth. Rangers games are now primarily on 105.3 The Fan, which has been the Rangers' flagship station since the 2015 season. At the conclusion of the 2018 season, Nadel joined a handful of broadcasters to call Major League Baseball games for 40 years, with the added distinction of calling all of them for one franchise. Among Nadel's most memorable calls was the 5000th strikeout of Nolan Ryan's career on August 22, 1989. His main home run call is "That ball is history!" The arrival of Rubén Sierra in Texas motivated Nadel to learn Spanish. Nadel is now a fluent Spanish speaker, having taken part in Spanish-language game broadcasts in a number of Latin American countries.
Nadel appeared as the Rangers' radio announcer in the film The Rookie in 2002. Nadel is active in animal causes and was one of the founders of the first leash-free dog park in the DFW Metroplex at White Rock Lake in Dallas. He stages benefit concerts for non-profit organizations, including Focus on Teens and Cafe Momentum, and is an active advocate for mental health organizations such as NAMI and The Campaign to Change Direction. Nadel is also the author of several books. In 2018, inspired after reading a rhymed radio ad, he began writing baseball-inspired limericks. His limericks have been published in a book titled Lim-Eric!.