Which is the correct grammar:
 " Thank you for electing Mike and me to the Board." or
 " Thank you for electing Mike and I to the Board." ?

The correct answer is:
"Thank you for electing Mike and me to the board."

In order to see how it is so, omit "Mike and" from the sentence and
you shall see that "I" do not belong in the sentence.  Omitting "Mike
and" from the sentence does not change the structure of the sentence.
In English "me" is the objective case of "I" and can be used as a
direct or indirect object of a verb.  In this sentence, the verb is
"to elect," and the objects are "Mike and me."
Hope this helps.

This is how I was taught. TY for a quick and complete answer.