The daughter of John Nevill Jackson and Viva Christian Thérèse (née Blomfield) Jackson, she was educated at the University of East Anglia, the University of Manchester and the University of Bristol, where she took her Master's degree.
In 1999, she was appointed director of the Scottish Arts Council, where she was responsible for the public funding of the arts in Scotland. After two years in post, she left, after falling out with SAC chairman James Boyle.
In 2002, she became the founding artistic director and chief executive of the Artes Mundi Prize, a contemporary art prize in Wales, a position which she held until 2010. Simultaneously, she was also the chair of the Edinburgh Art Festival between 2005-10.
Appointed to her position as CEO of Iniva in 2009, she has continued to uphold the organisation's remit to bring leading black, Asian, African, Middle-Eastern, Caribbean, Oceanic and Latin American contemporary artists from around the world to the London venue, which had become, in 2007, the capital's first purpose-built, publicly funded international contemporary art gallery since the Hayward Gallery in 1968.
Speaking to LabKulture in 2011, Jackson stated that her aim at Iniva was, "to diversify how we look at society – through the visual arts... poking society in the ribs a little bit and reminding us there are different view points, different histories that historically in Britain we haven’t always given a proper platform to."
During her time at Iniva, the organisation's Arts Council National Portfolio Organisation core funding was reduced by 75%.
- Francesco Bonami; Joel Snyder; Tessa Jackson (2004). Fiona Tan: Correction. Museum of Contemporary Art, Chicago. ISBN 9780933856844.
- Tessa Jackson, ed. (2004). Artes Mundi. Seren. ISBN 9781854113696.
- Tessa Jackson; Owen Sheers; Ann Jones (2011). Tim Davies. Riding House. ISBN 9781905464432.
- Tessa Jackson; Jane Lee (1993). Tracy Mackenna: Purposeful Invisibility. Arnolfini. ASIN B0041U7ULC.
- Sophie Bowness; David Chipperfield; Frances Guy; Jackie Heuman; Tessa Jackson; Simon Wallis; Gordon Watson (2011). Barbara Hepworth: The Plasters The Gift to Wakefield. Lund Humphries. ISBN 9781848220669.
- Profile of Tessa Jackson OBE Archived 2015-09-23 at the Wayback Machine, debretts.com; accessed 5 November 2017.
- "Iniva, Institute of International Visual Arts, Appoints Tessa Jackson as CEO". 4 November 2009. Retrieved 3 February 2014.
- Tessa Jackson stands down, artsprofessional.co.uk; accessed 4 November 2017.
- Hazel Colquhoun (2006): History of the redevelopment of the Arnolfini, publicartonline.org.uk; accessed 5 November 2017.
- Keith Bruce. "Jackson to take over at Scottish Arts Council", heraldscotland.com; accessed 5 November 2017.
- Arts chief to quit after ow with chairman, scotsman.com; accessed 5 November 2017.
- Artes Mundi congratulates founding Artistic Director Tessa Jackson
- "The arts go on show in Edinburgh", bbc.co.uk; accessed 5 November 2017.
- Swantje Diepenhorst. London interview with Tessa Jackson - CEO of Iniva, LabKultur.tv; accessed 5 November 2017.
- Morgan Quintance. "Iniva: Fit for Purpose?", Art Monthly, 22 December 2014.