They are claiming the Washington Post falsely accused him and other students of racist acts as well as instigating a confrontation with Native American protester Nathan Phillips at a Washington, D.C.pro-life rally in January.
The suit was filed in US District Court in Kentucky, Reuters news agency reported, and it states that the sum - which is for "compensatory and punitive damages" - is what Amazon.com founder and the world's richest man Jeff Bezos paid to buy the newspaper.
Phillips, a Native American elder, was attending an Indigenous People's March at the National Mall at the same time.
"It was getting ugly, and I was thinking: I've got to find myself an exit out of this situation and finish my song at the Lincoln Memorial", Phillips told the Post.
The US teenager at the centre of a viral video controversy featuring a Native American in Washington is now suing a media organisation for $250 million.
Following the incident, a statement was released by a public relations firm on Sandmann's behalf in which he claimed he had been singled out by Phillips and that he was only "helping to [defuse] the situation".
The Washington Post stands accused in the lawsuit of practicing "a modern-day form of McCarthyism" and for using its financial resources to publish false and defamatory print and online articles to smear a kid.
Other Covington students could be seen in the background.
But longer videos of the incident showed Mr Philips and a small group with him had intervened to place themselves between the students and a street preacher from the Black Israelites, who was abusing the students through a megaphone.
The lawsuit claimed the WaPo "ignored basic journalist standards", when reporting on the story.
The Jan. 18 incident was the subject of a viral video and numerous media reports, after, the complaint alleges, a short video of the encounter was initially perceived to be showing Sandmann and other Covington students - many of them wearing red "Make America Great Again" hats - as blocking Phillips' path and mocking him as he beat a drum.
"To make these charges and lawsuits and say it's all political and The Post hates Trump and that's why this was done, it was malice, I think that's a much tougher case to make in a courtroom", Kurtz said.
The Washington Post is reviewing a copy of the lawsuit and plans to "mount a vigorous defense", according to spokeswoman Kristine Coratti Kelly.
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