Jack Teixeira, who reportedly shared the files in an online gaming chatroom, faces charges under the Espionage Act.
Aerial footage showed officers making an arrest at Mr Teixeira’s family home in Dighton, Massachusetts.
The documents he leaked revealed intelligence about the war in Ukraine and US spying on allies.
Footage of the arrest in the town of 8,000 people about an hour south of Boston shows a young man, believed to be Mr Teixeira, walking backwards with his hands raised to armed FBI officers. He was handcuffed and led to a vehicle.
Roads in the area were blocked by police officers during the arrest.
“There were about six to eight Army guys with rifles walking around,” local resident Dick Treacy told Reuters news agency. “This is a very quiet area.”
Mr Teixeira is expected to make his first court appearance in Boston on Friday.
He was listed as 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 had been 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 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 said he went to school with Mr Teixeira, told Reuters he was surprised 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.
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 chatroom whose roughly two dozen members swapped “memes, offensive jokes and idle chitchat” and prayed and watched films 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.