He worked as a catechist and taught at the Salesians' major seminary in Altamira. He was later rector of various Salesian colleges and a member of his congregation's General Council, with responsibility for the Latin American, Caribbean and Pacific region.

On 23 October 1989 he was appointed titular Bishop of Utimmira and Vicar Apostolic of Puerto Ayacucho, receiving episcopal ordination from the Holy Father on 6 January 1990. 

On 27 May 1992 he was named Apostolic Administrator ad nutum Sanctae Sedis of San Fernando de Apure.

He was promoted to Archbishop of Caracas on 27 May 1995 and was Chancellor of Andrés Bello Catholic University andhonorary President of the Episcopal Conference of Venezuela.

Created and proclaimed Cardinal by John Paul II in the consistory of 21 February 2001. Titular church Santa Maria Domenica Mazzarello.

Card. Ignacio Antonio Velasco García died on 6 July 2003.