The former president vowed to "take America back" as he cemented his place as the party's frontrunner for November's election.
And the margin of victory put the US and the rest of the world on notice of how popular Trump remains with Republican voters.
It sets up a November 5 contest to be more explosive than Bonfire Night and fraught with complexities.
Both politicians would be the oldest president to win an election.
Biden, 81, who would be 86 by the time a second term finished, has been seen stumbling at events and committing several gaffes.
While Trump, no spring chicken at 77, has 91 criminal charges levelled against him.
But that did not appear to put off voters in Iowa on Monday as Trump saw off his closest rivals Ron DeSantis and Nikki Haley.
He won more than half of the votes in the state, confirming predictions he would begin his third presidential campaign with a telling victory.
In the lowest-turnout caucus in 25 years, voters had endured lifethreatening cold weather and dangerous driving conditions to meet in hundreds of schools, churches and community centres.
Those who ventured out delivered a roughly 30-point win for Trump that smashed the record for an Iowa Republican caucus and tightened Trump's grip on the party's nomination. However, it is still several months before the party's standard bearer can be confirmed.
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