Kevin Harpham, 37, entered his plea in US District Court in Spokane, Washington, days before he was due to go on trial and as part of his deal with prosecutors agreed to their characterisation of him as a white supremacist.
Under the plea deal, Harpham faces a sentence of between 27 and 32 years in prison and a life term of court supervision once he is released.
The agreement is subject to court review and formal approval before final sentence. Harpham was arrested at his Colville, Washington, home on 9 March.
The unattended backpack bomb, with wires visible, was discovered on a downtown Spokane bench along the parade route by three city workers who notified police about 30 minutes before the march was scheduled to begin, according to the FBI.
The 17 January parade, on the national holiday honouring the slain American civil rights leader and attended by about 2,000 people, was rerouted while the city's bomb disposal unit was summoned and safely neutralised the device.
No one was hurt, but the bomb was capable of causing serious injury or death had it exploded, the FBI said.
The shrapnel bomb, described as an "IED" (improvised explosive device) in court documents, consisted of a steel pipe packed with gunpowder and fishing weights coated with an anticoagulant chemical used in some rat poisons.
The bomb was rigged to be detonated by remote control using a car alarm key fob.
A camera seized during a search of Harpham's home contained deleted digital photographs of the march, including some Harpham took of himself at the parade, according to the documents outlining the plea deal.
Investigators also found racist messages and comments from Harpham, written under the pseudonym "Joe Snuffy," posted on the white supremacist website Vanguard News Network Forum.
Harpham "has told others about his racist beliefs and is a white supremacist and white separatist," the documents say.
Harpham, who served at the Fort Lewis Army base near Tacoma, Washington, from 1996 to early 1999 as a fire-support specialist, was identified by the Southern Poverty Law Center, an Alabama-based civil rights group, as having been a member of the neo-Nazi National Alliance in late 2004.
He pleaded guilty to the attempted use of a weapon of mass destruction and "attempt to cause bodily injury with an explosive device because of actual or perceived race, colour and national origin of any person." Two other charges he faced were dropped as part of the deal.