The Category 4 storm is making its way onto the state after laying waste to a number of islands and leaving at least 24 dead in the Caribbean.
Mr Drake was filmed by fellow storm chaser and meteorologist Simon Brewer. Shortly after posting the footage of Mr Drake, Mr Brewer also posted a picture of a handheld anemometer with a wind speed reading of 117mph.
The pair are part of a group of professional "storm riders", who pursue extreme weather phenomena.
Previously Mr Brewer has documented tropical cyclones including Hurricane Katrina and Hurricane Ike and hybrid super storm, Hurricane Sandy, in a career spanning over 15 years.
The video is some of the first footage of Irma hitting Florida. The hurricane is now heading up the west coast of the peninsula, with cities Tampa and St. Petersburg expected to bear the brunt.
Over 5 million people have been told to evacuate various areas of Florida in the last few days. Many of those who cannot escape to safer locations have crammed into designated shelters as they brace for the storm.