Stephen Espalin, 57, could get five years in prison when he appears before a federal judge Thursday, the South Florida Sun Sentinel reported.
He was arrested in 2010 after he told Secret Service agents at a Boca Raton hospital that he had sent a bomb to the White House and hoped it would kill Obama, his wife and children and their dog.
"Espalin stated that he hoped the explosive device would kill the president of the United States because he did not approve of his political leadership," his plea agreement said.
Espalin told police in Memphis in 2001 he planned to use a bomb against Bush. He received an 18-month sentence and was ordered to get psychiatric treatment.
Espalin later said the threat was not serious, telling the sentencing judge he was "mad and upset."
"He stated that a part of him wants to continue making the threats because he enjoys the attention that he is getting," an appeals court judge said in 2009.
Espalin has been diagnosed as having borderline personality disorder. He has a long history of arrests -- 59 by 2001 -- under different names and Social Security numbers.