“I am excited after getting the news," Singh, 40, told ucanews.com.
Singh, who with the guidance of the Catholic priest became a Christian while serving a 12-year jail term, is busy preparing his travel documents.
The priest, popularly known as Swami Sadanand, was instrumental in counseling Singh after the killing.
The Carmelite of Mary Immaculate regularly met him in jail.
The invitation to the Vatican is to attend a special screening of a documentary on the killing, called The Heart of a Murderer, by award winning Australian-Italian director Catherine McGilvray.