The best-selling author of Girl, Woman, Other will replace Dame Marina Warner as the figurehead of the literary organisation when she steps down at the end of 2021.
Evaristo will make history as the second woman and first writer of colour to be appointed to the role.
The charity, founded in 1820, says it aims to advance literature by honouring and supporting emerging and established writers and through creating a bridge between authors and audiences to engage as many people as possible.
Evaristo said: "I am deeply honoured to take on the role of the new president of the Royal Society of Literature.
"Although founded two hundred years ago, the Society is boldly embracing the twenty-first century as a great champion of the possibilities of a more egalitarian culture for literature.
"Storytelling is embedded in our DNA as human beings - it is sewn into the narrative arc of our lives, it is in our relationships, desires and conflicts, and it is the prism through which we explore and understand ourselves and the world in which we live. Literature is not a luxury, but essential to our civilisation.
"I am so proud, therefore, to be the figurehead of such an august and robust literature organisation that is so actively and urgently committed to being inclusive of the widest range of outstanding writers from every demographic and geographical location in Britain, and to reaching marginalised communities through literature projects, including introducing young people in schools to some of Britain's leading writers who visit, teach and discuss their work with them.
"I look forward to the next four years as the figurehead of such a wonderfully impressive organisation."
The author was the joint winner of the Booker Prize in 2019 for her novel Girl, Woman, Other, and was the first Black female author to top the paperback fiction chart in the UK.
Evaristo, who has also penned other popular books including Mr Loverman and The Emperor's Babe, was elected as a fellow to the RSL in 2004 and has been vice-president since November 2020.
During her time with the charity, she has also run workshops for young people and chaired many events and programmes including acting as vice-chair of the charity's governing council and chair of its programmes committee.
She is also currently the chair of the Society's Open Fellowship recruitment panel, was a panellist on the 40 Under 40 Fellowship initiative and helped launch the Sky Arts RSL Writers Awards which provides mentoring for emerging writers of colour.
Daljit Nagra, chair of the RSL said: "We are so proud to have Bernardine Evaristo as our President. She is a seminal writer. She is a trailblazer."
The charity, which celebrates its 201st birthday on Tuesday, has also announced the first 12 authors in the RSL international writers programme.
The writers recognised come from countries across the globe - from Antigua to China - and include Don Mee Choi, Annie Ernaux, David Grossman, Jamaica Kincaid, Yan Lianke and Amin Maalouf.
Alain Mabanckou, Javier Marias, Ngugi wa Thiong'o, Claudia Rankine, Olga Tokarczuk and Dubravka Ugresic are also among the chosen writers whose work ranges across essays, novels, poems, non-fiction and opera libretti.
The programme is a new award recognising the contribution of writers across the globe to literature in English, and the power it can have to transcend borders and bring people together.