Redman, who is both African American and Jewish American, was born in Berkeley, California, to jazz saxophonist Dewey Redman and Renee Shedroff. He was exposed to many kinds of music at the Center for World Music in Berkeley, where his mother studied South Indian dance. Some of his earliest lessons in music and improvisation were on recorder with gamelan player Jody Diamond.
He graduated from Berkeley High School, class of 1986, after having been a part of the award-winning Berkeley High School Jazz Ensemble for all 4 years of high school. In 1991, he graduated summa cum laude with a degree in Social Studies from Harvard University, where he was a member of Phi Beta Kappa Society. During college, he used his mother's maiden name, as Josh Shedroff.
Redman won the Thelonious Monk International Jazz Saxophone Competition, also in 1991, and began focusing on his musical career. Redman continued to develop his style throughout the 1990s, beginning with a sideman appearance on Elvin Jones' Youngblood alongside Javon Jackson (recorded at the Van Gelder Studio in April 1991), and following up with an appearance on his father Dewey's 1992 record Choices. On his second album as a leader, Wish, he was joined by a notable lineup consisting of guitarist Pat Metheny, bassist Charlie Haden, and drummer Billy Higgins; he would later tour this album as The Joshua Redman Quartet, featuring Christian McBride in place of Charlie Haden. He continued to work with various quartets, including one with pianist Brad Mehldau until forming a new trio, Elastic, with keyboardist Sam Yahel and drummer Brian Blade.
The trio debuted under the moniker Yaya3, producing one album under this name. The same group of musicians made up the core on Redman's Elastic album, before becoming known as the Joshua Redman Elastic Band. Some of his works were featured on The Weather Channel's Local On The 8s.
In addition to his efforts with Elastic, Redman was the artistic director of San Francisco's SFJAZZ Collective from 2004-2007. Redman has made a guest appearance on an episode of the TV show Arthur as the uncle of Francine, one of the main characters. The episode also depicts him in a boxing match against classic cellist Yo-Yo Ma. He worked with Yoko Kanno in the Japanese blues group, The Seatbelts that did the music for Cowboy Bebop. He also appeared on Reading Rainbow, episode 127 "Hip-Cat," in which Redman discussed with host Levar Burton the importance of music and how jazz had affected his life, which he followed with a live performance. Redman also performed on the soundtrack of the made for TV film "Love and Betrayal: The Mia Farrow Story" (1995).
Redman has also appeared on recordings and in live performances by Umphrey's McGee. On his album, Back East, Redman paid tribute to Sonny Rollins' 1957 album Way Out West, teaming up with musicians including Brian Blade, Christian McBride, Al Jackson, Joe Lovano, and his late father.