According to the documents, Corkins had thought about such an attack for years but "just never went through with it."
He purchased the gun used in the attack a week before at a Virginia gun store, where a French television crew taped him while doing a story about the widespread availability of guns in America, according to prosecutors.
He also went to the store the day before the attack for two hours of training.
U.S. Attorney Ronald Machen said Corkins' guilty plea "makes clear that using violence to terrorize political opponents will not be tolerated."
At the time of the shooting, Corkins lived with his parents in Herndon, Virginia, and volunteered at a Washington center for the lesbian, gay, bisexual and transgender community.
In August, FBI investigators said in an affidavit that investigators had interviewed Corkins' parents after the shooting, and they said their son "has strong opinions with respect to those he believes do not treat homosexuals in a fair manner."
The Southern Poverty Law Center has listed the Family Research Council as a hate group since 2010, pointing to what it describes as its anti-gay propaganda and legislative agenda.
On his nightly radio show on Wednesday, Family Research Council President Tony Perkins mentioned the plea deal and accused the Southern Poverty Law Center of playing a role in the shooting by inciting hatred and violence rather than fighting it -- a claim he has repeatedly made since the shooting.
"The Southern Poverty Law Center is dangerous. They are inciting hatred, and in this case a clear connection to violence," he said on the radio broadcast. "They need to be held accountable, and they need to be stopped before people are killed because of their reckless labeling and advocacy for homosexuality and their anti-Christian stance."
A spokeswoman for the center declined to comment on the plea deal or the research council's comments, but referred to a statement from the organization last year, standing by its designation of the Family Research Council as a "hate group."
"As people who care about human dignity, we have a moral obligation to call out the FRC for its demonizing lies and incendiary rhetoric about the LGBT community," the statement said. "The fact that we list the FRC as a hate group because of its demonizing propaganda does not make us the hateful one. Spreading demonizing lies is what is dangerous, not exposing them."