The idea of a national free legal services organisation was mooted at a national conference of lawyers held in 1992 under the auspices of the Bangladesh Bar Council. As a follow up to this idea, BLAST was established as a not-for-profit Trust, with a Board of Trustees comprising eminent jurists, lawyers, and former judges of the Bangladesh Supreme Court. It was incorporated in May 1993 with the Registrar of Joint Stock Companies as a company limited by guarantee, and was registered in December 1993 with the NGO Affairs Bureau of the Government of Bangladesh.
In 1994 Unit Offices were set up in five divisional headquarters i.e., Dhaka, Chittagong, Rajshahi, Khulna and Barisal. In 1995 one Unit Office at Sylhet divisional headquarter and the first two District units were established in Mymensingh and Noakhali. Three district Unit Offices in Jessore, Rangpur and Comilla were then established in 1996. Unit Offices were established in Bogra and Patuakhali in 1997 Pabna, Tangail and Kushtia in 1999, Dinajpur and Faridpur in the year 2000, and Rangamati in the year 2005 reaching all the 19 'old' districts.
BLAST commenced its activities in July 1994 by setting up its National Headquarters in Dhaka. It grew rapidly in response to increasing demand for its services given the lack of available and effective free legal services for the overwhelming majority of poor and disadvantaged persons seeking redress. Within less than a decade, BLAST has emerged as the largest specialized legal services organization in Bangladesh, and in a comprehensive and holistic approach, combining access to non-formal dispute resolution as well as judicial remedies right across the legal system, from the lower courts to the apex court.
BLAST initially received financial support from the Ford Foundation and the Asia Foundation, and now does so from DFID, NORAD, OXFAM, NOVIB and DANIDA.