He is being charged with five federal crimes, Sessions shared.
Cesar Sayoc is seen in this undated booking photo, released by the Broward County Sheriff's office and provided by the Associated Press, in Miami.
"These terrorizing acts are despicable and have no place in our country", Sessions told reporters.
It was not clear whether Sayoc had been formally charged in the rash of devices addressed in recent days to Democratic figures including former President Barack Obama, former Vice President Joe Biden and Hillary Clinton.
Later, two more were discovered in California.
The incidents come less than two weeks before the U.S. mid-term elections, with politics highly polarised.
"This last question that I thought Wray gave a very weird answer to when he was asked "when did you tell the White House, when did you tell the president", and [he] wouldn't answer that", said Miller, pointed out that in reality the answer should always be "immediately".
'We will not tolerate such lawlessness, especially not political violence'.
Cesar Sayoc, 56, of Ft. His Twitter page has also been found, which contains several pro-Trump and anti-liberal posts, as well as posts bashing "Hollywood slime" like George Clooney, Oprah Winfrey and Eminem. MSNBC reported that he was registered as a Republican Party member.
In the 2002 bomb threat case, Sayoc pleaded guilty to the felony without a trial and was sentenced to probation, the records show.
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Sayoc, of Aventura, was arrested Friday morning at a business in Plantation, Florida, some 30 miles north of Miami, a source said. He also had several arrests for theft in the 1990s.
Court records show Mr Sayoc filed for bankruptcy in 2012 while he was living with his mother. He did not graduate, the spokeswoman added.
Fingerprint and DNA evidence was used to identify the suspect, but Federal Bureau of Investigation Director Christopher Wray cautioned that the arrest did not necessarily end the threat.
A van seized in connection with Savoc's arrest was covered in far-right stickers, many featuring images from prominent conservative memes.
What did Mr Trump say about the bombs?
Trump called for a cooling of political rhetoric as he also praised law enforcement for the arrest.
The Department of Homeland Security has said there are no links to worldwide terrorism.
"We will prosecute. them to the fullest extent of the law". "We must never allow political violence to take root in America".
On the same day, officials removed a mail bomb in CNN television offices addressed to John Brennan, a former director of the Central Intelligence Agency under Obama. "Republicans, go out and vote!" said Trump.
How did the bomb threat unfold?
The first package was detected on Monday at the NY home of billionaire philanthropist and Democrat donor George Soros. They consisted of "approximately six inches of PVC pipe, a small clock, a battery, wiring, and energetic material", which "gives off heat and energy" when initiated by "heat, shock or friction". The devices were being examined by technicians at the FBI's forensic lab in Quantico, Virginia. They have timers easily bought at retail outlets.
While CNN was among the recipients of packages this week, the vast majority of tweets from the account linked to the suspect show screen grabs or videos of television news coverage depict segments from Fox News.