"The brothers read the instructions in 'Inspire', an online, English-language magazine that terror monitoring groups say Al Qaeda began publishing in 2010," Tsarnaev told investigators from his hospital bed in Boston, according to NBC News.
"The magazine has twice included articles on building bombs with kitchen pressure cookers, the method investigators say Dzhokhar and his brother, Tamerlan, used in the Boston attack," NBC added.
The Tsarnaev brothers are accused of planting the homemade bombs that exploded at the finish line of the Boston Marathon April 15, killing three people and injuring 180.
Tamerlan Tsarnaev, 26, was killed during a shootout with police in the Boston suburb of Watertown. Dzhokhar, 19, was apprehended after eluding a massive manhunt that saw the city of Boston and many of its suburbs shut down.
Fox News said a US official told it that the brothers "built the bombs with instructions from Inspire magazine" while CBS News said former New York Police Department bomb technician Kevin Barry told the network that the components used in the Boston marathon bombings were "a mirror image of what was printed on Inspire's pages".
Inspire is said to have published a special section titled "How to Make a Bomb in the Kitchen of Your Mom", in which the "simple steps to make pipe bombs and pressure cooker bombs" were spelled out, CBS said.
The online magazine is reported to have said in that posting that "the pressurized cooker is the most effective method".
Dzhokhar Tsarnaev's condition has now been upgraded from serious to fair, the Federal Bureau of Investigation (FBI) said.
US media reports said Dzhokhar told investigators that he and his brother acted alone in carrying out the attack and that they were motivated by religion.
Dzhokhar has been charged with one count of using and conspiring to use a weapon of mass destruction, namely an improvised explosive device "against persons and property within the US resulting in death", and one count of malicious destruction of property by means of an explosive device resulting in death.
Both charges carry the death penalty, the US Department of Justice said.
The teenager reportedly has been speaking to investigators from his hospital bed in Boston by nodding or shaking his head, or giving monosyllabic answers. An injury he sustained to his neck has left him unable to speak.