Irma is set to intensify as the eye of the storm approaches the Florida Keys, which will be hit around daybreak on Sunday.
Its 125mph winds will then move across the state and impact northwest Florida on Monday.
A state of emergency and a curfew is in place in Miami Beach and more than six million people have been ordered to evacuate the state.
Tornado warnings are in place for some areas and a deluge of 18 to 25 inches (46-64cm) of rain is expected.
The state's entire west coast is at risk of storm surges that could reach 15ft (4.6m) above ground level.
Locals were warned the sea surges, which will come after the worst of the winds, would submerge their homes in some areas.
President Trump, speaking at Camp David, said: "It's a storm of enormous destructive power and I ask everyone in the storm path to heed all instructions and get out of its way."
He added: "Property is replaceable but lives are not, and safety has to come first."
Florida governor Rick Scott also gave a stark warning as the hours ticked down, urging people to be "aggressive to protect their family".
He said: "If you have been ordered to evacuate, you need to leave. Now.
"This is your last chance to make a good decision. Evacuations are in place in areas across the state... Do not put yourself or your family's life at risk, now is the time to do the right thing for your family."
Florida is "under a state of emergency", he declared, with curfews in place in Miami Beach for the next three nights.
More than 170,000 homes and businesses were without power late on Saturday night and that number could end up being millions, energy firms have warned.
More than 70,000 Floridians were also hunkering down in shelters, with authorities already making plans for temporary housing once Irma passes.
Attractions such as Disney World have shut their gates in preparation for the storm.
Irma was downgraded to a category three storm on Saturday, but is expected to regain its category four status as it moves over warm open water on its approach to the US.
It has already wreaked havoc in the Caribbean, where it killed at least 27 people, and caused significant damage to Cuba on Saturday.
Amid the devastation, Sky sources understand between 100-120 prisoners have escaped from a jail on the British Virgin Islands after it was partially destroyed.
France has also boosted its police presence on the islands of St Barts and St Martin as local officials struggle to control looting.
The bill for loss and damage could hit $120bn (£91bn) in the US and Caribbean, according to data modelling firm Enki Research.
Defence Secretary Sir Michael Fallon, who chaired a meeting of the UK Government's emergency COBRA committee, declared Britain's relief operation "well under way" with 500 troops in the region.
Efforts are focused on the British Virgin Islands, where police officers from 14 forces are due to arrive to help maintain law and order and assist with the search for missing people.
Sir Michael rejected criticism of the Government's response.
But some parts of the Caribbean were breathing a sigh of relief on Saturday as category four Hurricane Jose - with 145mph winds - moved away from the northern Leeward Islands.
The archipelago includes Antigua and Barbuda, Saint Martin and Anguilla, which have already been devastated by Irma.