Mondesir was born in Stepney, London, on 12 December 1964.
Mondesir began his career in 1984 as part of Ian Carr's workshops at the Weekend Arts Center. He worked with Courtney Pine between 1985 and 1989 and recorded with Kevin Eubanks in 1991. In the 1990s he accompanied musicians who were visiting the UK; these included Art Farmer, Hermeto Pascoal and John Scofield. He played with Pee Wee Ellis' Assembly in 1996. In the 1990s and early 2000s he was part of bands led by pianist Julian Joseph.
He was part of guitarist John McLaughlin's 4th Dimension Band for their To the One album, which was recorded in 2009. The band was also featured on the Live @ Belgrade DVD from 2008. Mondesir left the band in 2010.
With Michael Gibbs
- Nonsequence (Provocateur, 2001)
- Here's a Song for You (Fuzzy Moon, 2011)
- Back in the Days (Cuneiform, 2012)
With Julian Joseph
- The Language of Truth (EastWest, 1991)
- Reality (EastWest, 1993)
- Universal Traveller (EastWest, 1995)
With John McLaughlin
- The Promise (Verve, 1995)
- Industrial Zen (Verve, Universal 2006)
- To the One (Abstract Logix, 2010)
With Courtney Pine
- Journey to the Urge Within (Antilles, 1986)
- Traditions Beckoning (Antilles, 1988)
- Destiny's Song + the Image of Pursuance (Antilles, 1988)
- To the Eyes of Creation (4th & Broadway, 1992)
- Toni Childs, The Woman's Boat (DGC, 1994)
- Barbara Dennerlein, Hot Stuff (Enja, 1990)
- Pee Wee Ellis, What You Like (Minor Music, 1997)
- Kevin Eubanks, Turning Point (Blue Note, 1992)
- Kevin Eubanks, Spirit Talk (Blue Note, 1993)
- Andy Hamilton, Silvershine (World Circuit, 1991)
- Jazz Warriors, Out of Many One People (Antilles, 1987)
- Rita Marcotulli, Basilicata Coast to Coast (Alice, 2011)
- Jean-Michel Pilc, Live at Iridium New York (Dreyfus, 2005)
- Jean-Michel Pilc, New Dreams (Dreyfus, 2007)
- Andy Sheppard, Steve Lodder, Moving Image (Verve, 1996)
- Jean Toussaint, What Goes Around (World Circuit, 1992)
- Jesse van Ruller, European Quintet (Blue Music, 1997)
- Steve Williamson, A Waltz for Grace (Verve, 1990)
- Steve Williamson, Rhyme Time (Verve, 1991)
- Chilton, John (2004). Who's Who of British Jazz (2nd ed.). Bloomsbury. pp. 250–251.
- Micallef, Ken (June 2010). "Gratitude for Coltrane". DownBeat. p. 13.
- Myers, Mitch (October 2010). "John McLaughlin: & the 4th Dimension Live @ Belgrade". DownBeat. p. 62.
- Milkowski, Bill (January 2013). "John McLaughlin: Echoes from Then". DownBeat. p. 30.