By qualifying as a resident alien per the Substantial Presence Test by the end of the tax year. Because you were not a resident alien at the beginning of the year you be required to file a Dual Status return. See IRS Taxation of Dual-Status Aliens.
The income earned in Denmark would be reported on the Form 1040-NR and the income earned from the date you became resident alien on Form 1040. Some of the income in the U.S would be reported on the Form 1040-NR.
Per Taxation of Dual-Status Aliens you must file a Form 1040 if you are a dual-status taxpayer who becomes a residence in the United States during the year and who is a U.S. resident on the last day of the tax year. Write "Dual-Status Return" across the top of the return.
Attach a statement to your return to show the income for the part of the year you were not a resident. You can use Form 1040-NR - U.S. Nonresident Alien Income Tax Return, as the statement, but be sure to mark "Dual-Status Statement" across the top.
TurboTax does not support the Form 1040-NR. You will need to use Sprintax to file a Form 1040-NR. If you have questions you can contact Sprintax Help for assistance.
The Physical Presence Test and Bona Fide Residence Test would be used when you are completing the form for a Foreign Tax Credit. Because you will need to file a Dual Status return there will be no foreign income on your Form 1040.
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