You may have to jump through administrative hoops.
Florida's page about getting a drivers license covers your situation:
Drivers License for Non US Citizens
How to get Your Florida Drivers License
The first step to getting a Florida Drivers License if you are not a US Citizen is to provide the required identification.
You must show proof of birth date and social security number (if issued.) Immigrants and non-immigrants have different identification requirements. Once the state of Florida verifies identity and legal status, a drivers license or identification card will be issued within 30 days from the DMV and mailed to the address on the driver record.
The Florida DMV has a reciprocity program meaning you do not have to take driving skill exams if your drivers license is valid from: United States or its Territories; United States Military; Canada, France, Germany, Republic of China or South Korea. For all other countries, you will need to complete DMV Test (Road Signs, Traffic Laws) and pass the behind-the-wheel driving exam.
Completing the Required First Time Driver Course
If you do not have a valid drivers license from the United States or a Foreign Country then you must complete the 4 hour Drug and Alcohol Traffic Awareness (DATA) Course, DMV Exam (Road Signs, Traffic Laws) and pass the behind-the-wheel driving test. You must complete the DATA Course before going to a DMV office, it's available online from approved providers. The written DMV Test (Road Signs, Traffic Laws) is available online for ages 14 to 17 from DMV approved schools. Age 18 or older must take the DMV Test at a DMV office.
Thus, you can shortcut the process if your EU drivers license comes from one of the listed countries. If it was not issued by one of the listed countries, then you must complete the entire application process.