The NYPD also announced it was investigating a "suspicious package" in midtown Manhattan on Friday morning.
Fingerprint and DNA evidence helped identify the suspect, officials said.
Sayoc is now facing charges of "transporting explosives across state lines, illegally mailing explosives, threatening former presidents and others, threatening interstate communications and assaulting federal officials", according to the Washington Post. Sessions said additional charges may come later.
In the hours before Sayoc was taken into custody, he was doing what he enjoyed: spinning Top 40 hits overlooking the stage at the Ultra Gentlemen's Club in Palm Beach, Florida.
The arrest of a Florida man fell in line with Homeland Security Secretary Kirstjen Nielsen's comments Thursday, in an interview with Fox News Channel, acknowledging that some of packages originated in Florida.
News of the arrest comes as the number of packages intercepted across the country grew to 14. One of the 14 explosive packages discovered last week was addressed to Biden.
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U.S. justice department officials said the bombs were "not hoax devices" and warned there could be more still undiscovered. Hillary Clinton and former President Bill Clinton, former VP Joe Biden, former Attorney General Eric Holder, Rep. Maxine Waters, former Central Intelligence Agency director James Brennan (in care of CNN) and billionaire Dem contributor George Soros.
The common thread among them was obvious: Their critical words for Trump and his frequent, harsher criticism in return.
While none of Sayoc's makeshift bombs exploded and no one was injured, 11 people were killed in a mass shooting in a Pittsburgh synagogue on October 27.
"These are not hoax devices", Wray said of the bombs. But they were uncertain whether the devices were poorly designed or never meant to cause physical harm.
Sayoc's past is marked by encounters with law enforcement.
The Justice Department and FBI confirmed the arrest and had a press conference scheduled for later in the afternoon to give details about their investigation, which began with the first bomb delivered to billionaire liberal donor George Soros.
Speaking before his supporters at a North Carolina campaign rally later Friday, Trump called the attempted attacks "terrorist actions" that must be punished "to the fullest extent of the law".
Almost all of the other targets who were intended recipients of packages also turn up in derogatory or highly critical tweets, including Hillary Clinton, Eric Holder and Maxine Waters.