In the case of the priest saying the words, the priest is empowered to give them special weight and significance.
From Merriam-Webster's definition of empower:
1 : to give official authority or legal power to
// empowered her attorney to act on her behalf
The priest empowered the words "I now pronounce you husband and wife."
The priest was empowered to make the everyday phrase spiritually and legally binding.
Alternatively, if it really is a word that has to start with i, then the priest imbues the words with special significance.
From Merriam-Webster's definition of imbue:
1 : ENDOW sense 3
// Spanish missions imbue the city with Old World charm
— Scott Pendleton
Endow sense 3
: to provide with something freely or naturally
// endowed with a good sense of humor