The original frontmen of the band were the Casamance singers Balla Sidibe and Rudy Gomis who came from the melting pot of Casamance musical styles, and most famously Laye Mboup (killed in a 1974 car accident) who provided vocals in the Wolof griot style. His Wolof language lyrics and his soaring, nasal voice defined the sound of Baobab's early hits.

Barthelemy Attisso from Togo was a law student in Dakar, and a self taught musician, whose arpeggiated runs became instantly recognizable. With the saxophone of N'Diaye, this was the first core of the band. Issa Cissoko (Saxophone) and Mountage Koite (drums) were both from Maninka griot families, from Mali and eastern Senegal respectively. The original group was rounded out by the slow groove Latin styles of Latfi Benjeloum (rhythm guitar), who came from a Moroccan family exiled to Saint-Louis, Senegal, and Charlie N'Diaye (bass) from Casamance.

The group played an Afro-Cuban music fused with distinctly West African traditions. Unlike other Senegalese bands, they combined the Casamance harmonies and drumming from southern Senegal with melodies from Togo and Morocco to the Wolof tradition from northern Senegal.

Ndiouga Dieng took up the Wolof griot vocals after the death of Mboup, but many famous singers sat in. Thione Seck (who left the band for good in 1979 and is today a superstar solo artist), his younger brother Mapenda Seck and Medoune Diallo provided vocals off and on after the death of Mboup. Medoune Diallo is especially known for his Spanish vocals on hits like El son te llama, as a more Latin feel permeated the band's sound in the late 70s. In 1979 the Club Baobab closed its doors, and the band sought new venues.

Orchestra Baobab recorded 20 vinyl albums (mostly released as cassette tapes) between 1970 and 1985. But competition from Mbalax, a new funk inspired sound in the mid 1980s, overwhelmed Orchestra Baobab. By 1987, the band had broken up. Many of the members formed or joined other groups, but Barthelemy Attisso returned to Togo to practice law. In 2001 he hadn't played a guitar in thirteen years.

In 1982, they had recorded what was later to become their most famous album: Pirates Choice. The record was only released in 1989, but garnered much critical acclaim outside Senegal, thanks to its release in Europe by World Circuit records.

After disbanding in 1987 the group came back together in 2001 with persuasion from Youssou N'Dour and their record label, World Circuit. The popularity of Orchestra Baobab began to decrease during the late 1980s due to the popularization of mbalax, the percussive street style popularised by Youssou N'Dour. During that same year Orchestra Baobab re-release their 1989 album Pirates Choice as a double CD with 6 extra rare tracks and completed a world tour including Europe and America. Most of the original line up reunited to play London’s Barbican Centre in May 2001. Since then Orchestra Baobab has released two records.

In 2002 Orchestra Baobab released Specialist in All Styles which was produced by Senegalese superstar Youssou N'dour with guest appearances by Cuban singer Ibrahim Ferrer and N'dour himself. Ibrahim Ferrer was not an accidental choice: not only had Orchestra Baobab written a song lauding this grand figure of Cuban music (Hommage a Tonton Ferrer), but Ferrer's huge burst of international fame with the Buena Vista Social Club in the 1990s mirrors the resurrection of Baobab. In fact, the original plan for what became the Buena Vista Social Club was organized by British world music producer Nick Gold of World Circuit Records, the same man who re-released Pirates Choice.

Orchestra Baobab gained attention from American media in 2003 when musicians Trey Anastasio and Dave Matthews filmed a documentary named Trey and Dave go to Africa which aired on VH1. The two visited Senegal and performed with Orchestra Baobab during the program.

Orchestra Baobab performed at Live 8 in Johannesburg, a series of concerts to end poverty.

In October 2007 Orchestra Baobab released the album Made in Dakar on World Circuit Records, leading commentators to claim that Baobab had reclaimed their place as pioneers of African Pop.

In May 2009 the band released "La Belle Epoque", a double-album of unearthed recordings dating from the 1970s. The package included a biography by Radio France Internationale journalist Pierre René-Worms, focusing on the early years before the group split. Volume 1 comprises recordings made at Club Baobab, Dakar, in 1971, 1973 and 1976; volume 2 includes original recordings made in 1978 for the album Baobab à Paris, their first European recordings. There are also original versions of Sibam and El Son te llama, written by Medoune Diallo, On verra ça by Balla Sidibé.

After being separated for 15 years Orchestra Baobab reunited in 2001. The reunited group went on to win the award for best African artists and the critics' choice award at the 2003 BBC Radio 3 World Music Awards. The group won both awards for Specialist in All Styles, their first album since their split in 1987. In winning the Best African Artists award Orchestra Baobab beat the African musicians Kasse Mady Diabate and Tony Allen.