Yes, you have to report your non-U.S. income on your U.S. income tax return, Form 1040. All United States citizens and green card holders are taxed on their worldwide income regardless of in which country they are residing or in which country the income is earned.
The fact that the same income may also be subject to taxation in another country does not eliminate the obligation to report it on the U.S. income tax return. Of course, the taxpayer may receive a foreign tax credit for taxes paid to another jurisdiction, which may offset some of the burden of the double taxation. Be aware that the Foreign Account Tax Compliance Act (FATCA) requires foreign financial institutions to report on the foreign assets of their U.S. account holders to the Internal Revenue Service (IRS). Therefore, failure to properly include interest, dividends, capital gains, etc. on your U.S. income tax return from foreign accounts could lead to a Pandora's Box of scrutiny and audit issues, not to mention penalty assessments. Remember that in addition to reporting non-U.S. income on your U.S. tax return, there are other foreign reporting obligations (such as FinCEN Report 114 and Form 8938) with their own filing requirements that must be adhered to. The reporting of worldwide income on the U.S. income tax return is not new and has been part of the U.S. tax law for many years. However, requirements surrounding the reporting have gotten increasingly more complex.
If you have a foreign financial account(s) and/or foreign assets, do yourself a favor and consult with a tax professional to help navigate through the various tax filing obligations.