Citing top law enforcement officials, the New York Times said the two devices used flip phones and Christmas lights designed to trigger the explosive.
The blast, in the Chelsea area of Manhattan, injured 29 people.
Officials call it a terror act, but no motive or suspect has been identified.
The second device was found four blocks from the site of the explosion and was removed safely.
New York governor Andrew Cuomo said it appeared to be "similar in design" to the exploded device.
Both were different from a pipe bomb that detonated earlier on Saturday
on the route of a charity race in New Jersey, Mr Cuomo added. That explosion caused no injuries.
The unexploded second device was destroyed by police in a controlled explosion late on Sunday.