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What happens when a non-U.S. citizen who's been making money from the U.S. moves to the U.S.?
Its not for US citizens - its for US residents. If the US considers you as a tax resident - you'll be treated the same as a US citizen, regardless of your immigration status. The question is very unclear, since it is not mentioned whether your US sourced income "from the Internet" is sales in the US, sales on-line, services you provide, investments, or what else. All these are treated differently. For some kinds of US-sourced income you should have paid taxes in the US already, regardless of where you physically reside. For others - not. In any case, if you become US tax resident, you'll be taxed on your worldwide income, not only the $10K deposited in the US bank account. ALL of your income, everywhere in the world, must be declared to the US government and will be taxed. You should seek professional advice, before you move to the US, in order to understand your responsibilities, liabilities and rights. I suggest looking for a EA/CPA licensed in California and experienced with taxation of foreigners (look for someone in the SF or LA metropolitan areas). Keep in mind that there may be a tax treaty between the US and your home country that may affect your Federal (but not California) taxes.