"Welcome home!" is correct because "home" is an adverb of place in this sentence. It shows where the action occurs. Because you can't use a preposition with an adverb alone, "to home" is not possible.
"Welcome to home!" is never correct because "home" is a singular, count noun and requires a determiner, such as my, her, our, John's: Welcome to our home! You could use "the," but then additional information is necessary to define "home": Welcome to the home of the best pizza on the planet!