By Mike Wendling, BBC News
Jack Teixeira is reported to be the leader of an online gaming chat group where the files were leaked.
US officials said he will be charged under the Espionage Act, which makes it a crime to transmit classified defence information.
The documents revealed sensitive intelligence about the war in Ukraine and other countries around the world.
Aerial footage showed officers making an arrest at Mr Teixeira’s family home on Thursday.
It happened in Dighton, a town of 8,000 people about an hour to the south of Boston.
Footage of the arrest shows a young man, believed to be Mr Teixeira, walking backward towards armed FBI officers with his hands raised before he is handcuffed and led to a vehicle.
Roads in the area were blocked by police officers while the arrest was taking place.
“There were about six to eight Army guys with rifles walking around,” local resident Dick Treacy told Reuters. “This is a very quiet area.”
Mr Teixeira is expected to make his first court appearance in Boston on Friday.
He is a member of the intelligence wing of the Massachusetts Air National Guard, based at Otis Air National Guard Base in western Cape Cod.
According to his service record, obtained by CBS News, the BBC’s US partner, Mr Teixeira joined the force in 2019.
His official title is cyber transport systems journeyman and he holds the rank of Airman 1st Class – a relatively junior position.
In a brief statement on Thursday, US Attorney General Merrick Garland said the suspect was taken into custody “without incident”.
Mr Garland provided no further details on the investigation or the motive for the leaks.
At a separate news conference earlier in the day, defence department spokesman Brigadier General Pat Ryder said that the leak was a “deliberate criminal act”.
When asked how such a young airman had access to classified defence documents, Gen Ryder said that across the US military, personnel are entrusted “with a lot of responsibility at a very early age”.
“Think about a young combat platoon sergeant, and the responsibility and trust that we put into those individuals to lead troops into combat,” he said.
Eddy Souza, a 22-year-old man who claims he attended high school with Mr Teixeira, told Reuters he was surprised that his former classmate had been identified as the suspect in the leaks.
“He’s a good kid, not a troublemaker, just a quiet guy,” Mr Souza said. “It sounds like it was a stupid kid’s mistake.”
What was in the leaks?
Starting several months ago, at least 50 but perhaps more than 100 classified documents were posted on Discord – a social media platform popular with gamers.
The documents – which BBC News is examining – contain a range of intelligence assessments about the war in Ukraine, but also sensitive intelligence about countries around the world, including US allies.
A defence department spokesman said the Pentagon is continuing to work to “understand the scope, scale and impact of these leaks”.
In a statement, Republican congressman Mike Turner – the chairman of the House Intelligence Committee – vowed to “examine why this happened, why it went unnoticed for weeks, and how to prevent future leaks”.
On Wednesday, the Washington Post published an interview with one of the members of the chatroom where the documents initially appeared.
He described the leaker as a young, charismatic gun enthusiast in his early to mid-20s who worked at an unnamed military base.
The Post reported that the man was the leader of a Discord chat room, including roughly two dozen members who swapped “memes, offensive jokes and idle chitchat” and prayed and watched movies together.
The members included people from Russia and Ukraine and a number of other countries in Europe, Asia and South America, the paper reported.
At first the leaks were kept inside the small chatroom, but in early March members began posting them on other Discord servers, including ones dedicated to the game Minecraft and a Filipino YouTuber.
From there they were posted on the fringe message board 4chan and on the Telegram chat app, particularly on pro-Russia channels. In some cases they were altered to increase Ukrainian casualty counts.
The Air National Guard is the reserve of the US Air Force.
US President Joe Biden was briefed about Mr Teixeira’s arrest while on a trip to Ireland, White House officials have confirmed to CBS.