Jones, host of the far-right talk show Infowars, listed liabilities of at least $1 billion in a bankruptcy court petition.
A Connecticut jury in October ordered Jones to pay about $1 billion in damages to the families of the Sandy Hook victims for falsely claiming that the shooting was faked.
He was later ordered to pay an additional $473 million for promoting conspiracy theories about the shooting that killed 20 children and six adults.
Earlier this year, Jones was ordered by a Texas jury to pay $49 million in damages to Sandy Hook parents Neil Heslin and Scarlett Lewis. Jones later lost a bid to reduce the damages owed.
In the Texas and Connecticut cases, some relatives of the victims gave evidence saying that they had been harassed and threatened for years by people who believed the lies that Jones had spread on his show.
Jones's bankruptcy filing gives him breathing space from his creditors while he sorts out a repayment plan. The filing also alludes to the continuing bankruptcy of Free Speech Systems LLC, the parent company of Infowars.
His assets total no more than $10 million, the petition says.
On his show, Jones said he has less than $2 million to his name and would not be able to pay the roughly $1.5 billion that he owes.
A forensic economist at the Texas trial said Jones and Free Speech Systems have a combined net worth of up to $270 million.
The Associated Press contributed to this report