Hasan is charged with 13 counts of premeditated murder and 32 counts of attempted murder for the 2009 mass shooting at the Fort Hood military base, in which 13 people were killed and 29 others were wounded.
The letters were released days before Hasan's court-martial is due to start.
The letters, which were sent to Fox News and released Thursday, renounced Hasan's citizenship and abandon his military oath, KXXV-TV, Waco, Texas, reported.
"I Nadal Hasan, am compelled to renounce my oaths of alliances that require me to support or defend a man made constitution. I therefore formally renounce my oath of office as well as any other implicit or explicit oaths I have made. This includes my citizenship," Hasan wrote.
"There is an inherent and irreconcilable conflict. In an American democracy 'we the people' govern according to what 'we the people' think is right or wrong, even if it specifically goes against what All-Mighty God commands," Hasan wrote, asserting U.S. citizenship is not compatible with Sharia law.
Hasan's civil lawyer verified the documents and his signature.
Ohio bar shooting arrested, charged with murder
Duggar sisters unveil Christian dating rules in new book