Cardinal Gracias was born on 24 December 1944 in Bombay. He studied for the priesthood in Bombay and was ordained on 20 December 1970.
He was secretary to the Bishop of Jamshedpur from 1971 to 1976 before undertaking further studies in canon law in Rome at the Pontifical Urbanian University.
He returned to Bombay in 1982 and held various judicial roles.
Pope John Paul II appointed him as Auxiliary Bishop of Bombay on 28 June 1997. He was consecrated on 16 September 1997 by Cardinal Dias, with the titular see of Bladia.
Pope John Paul II then appointed him Archbishop of Agra on 7 September 2000. Pope Benedict XVI appointed him as Archbishop of Bombay on 14 October 2006 and made him a cardinal on 24 November 2007.