Three law enforcement officials identified the man as Cesar Sayoc, 56, of Aventura, Florida.
Video from television news helicopters showed federal agents and police examining a white van in the car park of a business in Plantation, Florida.
The van had several stickers on the windows, including American flags.
Earlier on Friday, authorities said suspicious packages addressed to New Jersey senator Cory Booker and former National Intelligence director James Clapper - both similar to those containing pipe bombs sent to other prominent critics of President Donald Trump - had been intercepted.
The discoveries further spurred a coast-to-coast investigation as officials scramble to locate a culprit and possible motive amid questions about whether new packages were being sent or were simply surfacing after a period in the mail system.
The devices have targeted well-known Democrats including former president Barack Obama, ex-vice president Joe Biden, Hillary Clinton and former attorney general Eric Holder.
Mr Trump said later that the suspect will be prosecuted to the “fullest extent of the law”, and added: “We must never allow political violence to take root in America.”
The FBI said the package to Mr Booker was intercepted in Florida, and one discovered at a Manhattan postal facility was addressed to Mr Clapper at CNN’s address. An earlier package had been sent to former Obama CIA director John Brennan care of CNN in New York.
Attorney general Jeff Sessions said the Justice Department was dedicating every available resource to the investigation, “and I can tell you this: we will find the person or persons responsible. We will bring them to justice”.
Mr Trump, on the other hand, complained that “this ‘bomb’ stuff” was taking attention away from upcoming elections and claimed critics were wrongly blaming him and his heated rhetoric.
Investigators are analysing the crude devices to reveal whether they were intended to detonate or simply sow fear just before election day on November 6.
Law enforcement officials said the devices, containing timers and batteries, were not rigged to explode on opening, but they were uncertain whether the devices were poorly designed or never intended to cause physical harm.
Homeland Security secretary Kirstjen Nielsen acknowledged that some of packages originated in Florida. One official said investigators homed in on a postal facility in Opa-locka, where they believe some packages originated.
The package addressed to Mr Booker was found during an oversight search of that facility, according to a law enforcement official.
Most of those targeted were past or present US officials, but others were sent to actor Robert De Niro and billionaire George Soros.
The bombs have been sent across the country - from New York, Delaware and Washington DC to Florida and California, where Democratic representative Maxine Waters was targeted.
They bore the return address of Florida representative Debbie Wasserman Schultz, the former chairwoman of the Democratic National Committee.
The common thread among the targets was obvious: their critical words for Mr Trump and his frequent criticism in return.
The president claimed he was being blamed for the mail bombs, complaining in a tweet: “Funny how lowly rated CNN, and others, can criticize me at will, even blaming me for the current spate of Bombs and ridiculously comparing this to September 11th and the Oklahoma City bombing, yet when I criticize them they go wild and scream, ‘it’s just not Presidential!’”
The package to Mr Clapper was addressed to him at CNN’s Manhattan address. The frequent Trump critic told CNN he was not surprised to be targeted and that he considered the actions “definitely domestic terrorism”.
The devices were packaged in manila envelopes and carried US postage stamps. They are being examined by technicians at the FBI’s forensic lab in Quantico, Virginia.
The packages stoked nationwide tensions ahead of the elections to determine control of Congress - a campaign both major political parties have described in near-apocalyptic terms. Politicians from both parties used the threats to condemn a toxic political climate and to lay blame.
Mr Trump, in a tweet on Thursday, blamed the “Mainstream Media” for the anger in society. Mr Brennan responded, tweeting that the president should “stop blaming others. Look in the mirror”.
The bombs are about 6in long and packed with powder and broken glass, according to a law enforcement official who viewed X-ray images. The official said the devices were made from PVC pipe and covered with black tape.
The first bomb discovered was delivered on Monday to the suburban New York compound of Mr Soros, a major contributor to Democratic causes, who has called Mr Trump’s presidency “dangerous”.