First, the "a" doesn't mean "to" - it's the definite article, same as in "o senhor" or "a senhora" [literally: 'the gentleman', 'the lady'].

I used to work in a protocol office, but in any case, all that I'm about to say about English usage can be found in the Chicago Manual of Style.

From the context, it looks as if this is DIRECT ADDRESS. In English the person's name isn't used; in Portuguese it is. Use of the third person to address the person to whom you are speaking seems alien for an English speaker, but it's a token of respect. A Portuguese speaker might call me "a senhora Muriel" to my face, using the third person out of deference. whereas in English we would never use an honorific when speaking directly to a person.

If it's a letter or an envelope, the address is usually written "H.E.," but it can also be written out as "His Excellency". Thus:

H.E. Jphn Jones
Ambassador of Cyberspace to the United States
1234 Any Street
Washington, D.C.

Excellency:

I am pleased to inform you that ....




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Note added at 7 hrs (2007-12-07 07:35:09 GMT)
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In the body of the letter you may also say Your Excellency later below (but not immediately after saying the word in the opening line).