The library is named after the late Roja Muthiah who had originally collected about 50,000 books and 50,000 other items like periodicals, ephemera, wedding invitations, pamphlets and clippings. Roja Muthiah of Kottaiyur in Tamil Nadu’s Sivagangai district was a sign-board artist. Immediately after his premature death in 1992, the University of Chicago (UoC) launched a global effort to save the collection. It was moved to Chennai and institutionalised in 1994. Subsequently, in 2004, the RMRL Trust was formed and an MoU was signed with the UoC for the maintenance of the collection. After the objectives of the MoU were met, the entire collection was transferred to the RMRL Trust to expand, maintain, and carry out its objectives.

RMRL, which has taken up several preservation projects, was initially funded by the National Endowment for the Humanities, the Ford Foundation, the Wellcome Trust for the History of Understanding Medicine, the Endangered Archives Project, the TATA Trusts, the India Foundation for the Arts, the National Archives of India, the Tamil Nadu Government and several individuals and CSR initiatives.

RMRL expanded its activities from collection, development, cataloguing and preservation of books to conserving books and conducting public lectures, seminars, exhibitions and research activities. RMRL started the Indus Research Centre (in 2007) and the Centre for Study in Public Sphere (in 2021).

Now the library functions on the premises that have been leased to it by the Government of Tamil Nadu. The State government supports the library with recurring grants since 2023 to sustain some of its major library activities.

RMRL is considered to be a culturally significant institution that showcases the civilisational heritage of Tamil and brings people together on a common platform for intellectual deliberation. The organisation collaborates with world-renowned institutions and is in line with best practices of activities relating to libraries, archives and museums.