Rambachan was born in Trinidad. Both his grandfathers were Hindu priests, who remained faithful to Hinduism, despite British pressures. At high school, he was impressed by Swami Vivekananda. After completing his undergraduate studies, Rambachan studied Advaita at Sandeepany Sadhanalaya, a Hindu seminary of the Chinmaya Mission in Mumbai, India, with Swami Dayananda Saraswati:
Rambachan completed his undergraduate studies at the University of the West Indies, St. Augustine, Trinidad. He received his M.A. (Distinction) and Ph.D. degrees from the University of Leeds, in the United Kingdom, where he researched "classical Advaita epistemology and, in particular, the significance of the śruti as a source of valid knowledge (pramāṇa) in Śaṅkara."
Since 1985 Rambachan has been teaching in the Department of Religion at St. Olaf College, Minnesota, USA, where he "continued my research and writing on Advaita, the Hindu tradition in a global context, Hindu ethics, Hinduism and contemporary issues and interreligious dialogue."Since 2013, Professor Rambachan has been Forum Humanum Visiting Professor at the Academy for World Religions at Hamburg University, Germany.
Rambachan is a Professor of Religion at St. Olaf College, Minnesota, USA. He has been teaching at St. Olaf since 1985.Rambachan is a Hindu and was the first non-Christian chair of the Religion Department at this Lutheran college. He is a member of the Theological Education Steering Committee of the American Academy of Religion, the Advisory Council of the Centre for the Study of Religion and Society, University of Victoria, BC, Canada, an advisor to Harvard University's Pluralism Project and a member with Consultation on Population and Ethics, a non-governmental organization, affiliated with the United Nations.
Rambachan is very involved with interreligious dialogue and more specifically, Hindu-Christian dialogue. He continues to participate in interreligious activities, both nationally and internationally. He is an active member and participant in the dialogue program of the World Council of Churches and participated in the last four General Assemblies.
He has traveled and lectured in Norway, Switzerland, Germany, Australia, Mauritius, South Africa, Kenya, India, Trinidad, Brazil, The Vatican, Japan, Italy, Spain, Canada and the United Kingdom. A series of 25 lectures was broadcast internationally by the BBC. Rambachan also led the first White House celebration of the Hindu Festival of Diwali in 2003. He continues to return to Trinidad on a yearly basis and was awarded the Chaconia Gold Medal, Trinidad and Tobago's second highest national honor for public service.Rambachan, Anantanand (1991). Accomplishing the accomplished: the Vedas as a source of valid knowledge in Śankara. [Honolulu]: University of Hawaii Press. ISBN 0-8248-1358-8.
Rambachan, Anantanand (2006). The Advaita worldview: God, world, and humanity. Albany, N.Y: State University of New York Press. ISBN 0-7914-6852-6.
Rambachan, Anantanand (1994). The limits of scripture: Vivekananda's reinterpretation of the Vedas. [Honolulu]: University of Hawaii Press. ISBN 0-8248-1542-4.
Rambachan, Anantanand, A Hindu Theology of LIberation: Not Two Is Not One, Albany: State University of New York Press, 2015. 230 pages. ISBN 978-1-4384-5455--9