Fr Joseph Palanivel Jeyapaul was accused of abusing a teenage girl whilst working in the US in 2004 but he travelled back to India before a criminal charge was made in 2006.
He had been urged to return to America to face the charge but in 2011 authorities made an official request for his extradition.
Fr Jeyapaul challenged the order but yesterday a court in Delhi refused his appeal and approved his extradition.
The 59-year-old has been held in an Indian jail since soon after the initial extradition request was made.
He denies the accusation.