Moving savings to the US is normal. The two things that cost people money are poor exchange rates and missing paperwork.
There is no limit on how much money you can bring. But if you carry more than $10,000 in total (US dollars, other currencies, traveler's checks, money orders or similar), you must declare it when you enter or leave the US.
Fill in FinCEN Form 105 (the currency report). You can do it online before travel and print it, or ask the officer at customs for a paper form.
Tell the customs officer when you arrive. Answer "yes" to the money question.
If you do not declare it, the government can take all of the money and fine you. Do not split cash among family members to stay under $10,000.
A wire transfer sends money from your bank at home to your US bank through the international SWIFT network.
Get from your US bank: the bank name and address, your account number, the SWIFT/BIC code, and sometimes a routing number for incoming wires.
Give these to your bank at home, with your name exactly as on the US account.
Expect fees from your bank, sometimes from a middle bank, and an incoming wire fee at your US bank.
The money usually arrives in 1 to 5 business days.
Online services (for example Wise or Remitly) often give a better exchange rate than banks. Compare the total dollars that arrive, not only the fee. Some have limits for large amounts.
Keep proof of source of funds
US banks must ask questions about large or unusual deposits. Keep:
Bank statements from home showing the money.
Papers showing where it came from: a property sale, salary, savings, or a gift letter from a parent.
Proof of any tax you paid at home.
This also helps with visa, green card and loan applications later.
Moving your own savings is not income, so it is not taxed again. But if you are a US tax resident (see the tax residency guide) and receive gifts or inheritance from a non-US person totaling more than $100,000 in a year, you must report it on IRS Form 3520. There is usually no tax, but missing the form has penalties.
Your home country may also have limits on sending money out. Check before you leave.
Choosing the bank's exchange rate without comparing.
Typing the name differently from the US account, which can send the wire back.
Throwing away statements from home.