Devika Rani Chaudhuri was born into a Bengali family in Waltair near Visakhapatnam in present-day Andhra Pradesh, into an extremely affluent and educated Bengali family. Her father, Colonel Manmatha Nath Chaudhuri, was the first Indian Surgeon-General of Madras Presidency and a nephew of Rabindranath Tagore.  Her mother, Leela Devi Choudhary, came from an educated family and was a grand-niece of Tagore. Devika's father's brothers were Ashutosh Chaudhuri, Chief Justice of Calcutta High Court, Jogesh Chandra Chaudhuri, a prominent Kolkata-based barrister and Pramatha Chaudhuri, the famous Bengali writer.  Devika Rani was related through both her parents to the poet and Nobel Laureate Rabindranath Tagore. Her father, Manmathnath Choudhary, was the son of Sukumari Devi Choudhary, sister of Rabindranath Tagore. Devika's mother, Leela Devi Chaudhuri, was the daughter of Indumati Devi Chattopadhyay, whose mother Saudamini Devi Gangopadhyay was another sister of the Nobel laureate. Devika's father and maternal grandmothers were first cousins to each other, being the children of two sisters of Rabindranath Tagore.  Further, two of her father's brothers had also married their cousins: Prativa Devi Choudhury, wife of Ashutosh Choudhary, was the daughter of Hemendranath Tagore, and Indira Devi Choudhary, wife of Promatho Choudhary, was the daughter of Satyendranath Tagore. Devika thus had strong ties to Jarasanko, seat of the Tagore family in Kolkata and a major crucible of the Bengali renaissance.  Devika Rani was sent to boarding school in England at the age of nine, and grew up there. After completing her schooling in the mid-1920s, she enrolled in the Royal Academy of Dramatic Art (RADA) and the Royal Academy of Music in London to study acting and music. She also enrolled for courses in architecture, textile and decor design, and even apprenticed under Elizabeth Arden. All of these courses, each of them a few months long, were completed by 1927, and Devika Rani then took up a job in textile design.

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Devika Rani was related through both her parents to the poet and Nobel Laureate Rabindranath Tagore.