McFerrin was born in Manhattan, New York City in 1950, the son of operatic baritone Robert McFerrin and singer Sara Copper. He attended Cathedral High School in Los Angeles, Cerritos College, University of Illinois Springfield (then known as Sangamon State University) and California State University, Sacramento.

His mother Sara (Copper) McFerrin was a soloist and taught voice at Fullerton College in Southern California.

McFerrin's first recorded work, the self-titled album Bobby McFerrin, was not produced until 1982, when McFerrin was already 31 years old. Before that, he had spent six years developing his musical style, the first two years of which he attempted not to listen to other singers at all, in order to avoid sounding like they sounded. He was influenced by Keith Jarrett, who had achieved great success with a series of solo improvised piano concerts including The Köln Concert of 1975, and wanted to attempt something similar vocally.

In 1984, McFerrin performed onstage at the Playboy Jazz Festival in Los Angeles as a sixth member of Herbie Hancock's VSOP II, sharing horn trio parts with the Marsalis brothers. In 1986, McFerrin was the voice of Santa Bear in Santa Bear's First Christmas, and in 1987 he was the voice of Santa Bear/Bully Bear in the sequel Santa Bear's High Flying Adventure. On September 24 of that same year, he recorded the theme song for the opening credits of Season 4 of The Cosby Show.

In 1988, McFerrin recorded the song "Don't Worry, Be Happy", which became a hit and brought him widespread recognition across the world. The song's success "ended McFerrin's musical life as he had known it," and he began to pursue other musical possibilities on stage and in recording studios. The song was used as the official campaign song for George H. W. Bush in the 1988 U.S. presidential election, without Bobby McFerrin's permission or endorsement. In reaction, Bobby McFerrin publicly protested that use of his song, and stated that he was going to vote against Bush. He also dropped the song from his own performance repertoire.

At that time, he performed on the PBS TV special Sing Out America! with Judy Collins. McFerrin sang a Wizard of Oz medley during that television special. In 1989, he composed and performed the music for the Pixar short film Knick Knack. The rough cut to which McFerrin recorded his vocals had the words "blah blah blah" in place of the end credits (meant to indicate that he should improvise). McFerrin spontaneously decided to sing "blah blah blah" as lyrics, and the final version of the short film includes these lyrics during the end credits. Also in 1989, he formed a ten-person "Voicestra" which he featured on both his 1990 album Medicine Music and in the score to the 1989 Oscar-winning documentary Common Threads: Stories from the Quilt.

Around 1992, an urban legend began that McFerrin had committed suicide; it has been speculated that the false story spread because people enjoyed the irony of a man known for the positive message of "Don't Worry, Be Happy" suffering from depression in real life. But in reality McFerrin knew the song helped spread the message of positivity to the world abroad and was very proud of the work as a whole.

In 1993, he sang Henry Mancini's "Pink Panther Theme" for the 1993 comedy film Son of the Pink Panther. In addition to his vocal performing career, in 1994, McFerrin was appointed as creative chair of the Saint Paul Chamber Orchestra. He makes regular tours as a guest conductor for symphony orchestras throughout the United States and Canada, including the San Francisco Symphony (on his 40th birthday), the New York Philharmonic, the Chicago Symphony Orchestra, the Cleveland Orchestra, the Detroit Symphony Orchestra, the Israel Philharmonic Orchestra, the Philadelphia Orchestra, the Los Angeles Philharmonic, the London Philharmonic, the Vienna Philharmonic and many others. In McFerrin's concert appearances, he combines serious conducting of classical pieces with his own unique vocal improvisations, often with participation from the audience and the orchestra. For example, the concerts often end with McFerrin conducting the orchestra in an a cappella rendition of the "William Tell Overture," in which the orchestra members sing their musical parts in McFerrin's vocal style instead of playing their parts on their instruments.