You say " I'm home!" when you have just reached your house and want to let someone know it.
Or , just casually say "I'm back!" to have the same meaning .
Or, "I'm home" when you have just return to your country ( here , you consider your country as your home , like you have been away for a long time and getting emotional.( metaphoric))
At someone's house , you say "I'm here!"? " I have arrived"