Dear Excellency as a greeting in writing, Your Excellency when speaking TO him, and His Excellency when writing or speaking OF him.

Your Excellency:

When written at the beginning, it's Dear[ no His OR Your ] Excellency. In the body of the letter , it's Your Excellency.

"Your Excellency" is used when you are addressing the person, like speaking or writing to them. "His Excellency" would be when you are talking to someone else about the person.

The Adjutant of His Excellency was created in 1969.

His Excellency - opera - was created in 1894.