The incident sparked a mass search of about 7000 US commercial airplanes.
"The FBI and the Department of Homeland Security's Transportation Security Administration have located and interviewed an individual believed to be responsible for the matter," the Justice Department said in a statement on Friday.
"Based on the investigation conducted thus far, this individual does not appear to pose any further threat to airline security."
In a separate statement the US Department of Homeland Security said authorities had been investigating the individual for months and linked him to the incidents in less than 24 hours.
"When the items were found last night, TSA quickly began a database search and linked the situations to an e-mail received by TSA's Contact Centre last month," the statement said.
"Somebody is saying: 'Look, you say your airplanes are much safer now, but look at me. I can put a box cutter in the bathroom.' They're trying to make a point"
The suspect is a 20-year-old North Carolina student, according to two sources who did not wish to be named.
The student is believed to have left packages containing modelling clay, bleach, box-cutters and taunting notes in six Southwest airplanes, although only two of the packages have been found, according to a Congressional source and a senior law enforcement official.
Southwest said it had completed inspections of all of its 385 aircraft by late Friday and found nothing further.
Items "intended to simulate a threat" were found on Thursday during routine inspections conducted on two Southwest jets in New Orleans, Louisiana and Houston, Texas, the airline said in an earlier statement.
Box cutters were among the weapons hijackers used in the 11 September, 2001 attacks that claimed nearly 3000 lives.
But officials said this week's incidents were intended not as terrorism but as a provocation of the Transportation Security Administration, the federal agency created after the 11 September attacks and charged with making US commercial airports safer.
"Right now, there is basically no evidence to suggest that this is related to terrorism," said Brian Roehrkasse, a Homeland Security spokesman.
Airlines have significantly beefed
up their security since 9/11
Sources said the student had been sending letters to the TSA for months, saying he planned to expose holes in the US travel security system, which has been increased since the 2001 attacks.
The Justice Department said legal proceedings against the suspect "are anticipated this Monday in United States District Court in Baltimore," Maryland.
It was not the first time cutters and other sharp objects have eluded security at US airports, according to Michael Barr, who trains aviation security professionals at the University of Southern California.
"Terrorists wouldn't leave a note," as the culprit or culprits in this case did, Barr said.
"Somebody is saying: 'Look, you say your airplanes are much safer now, but look at me. I can put a box cutter in the bathroom.' They're trying to make a point," he said.