The indictment accuses Stadd of steering money from an earth science appropriation to Mississippi State University, which was paying him as a consultant. Stadd is also accused of lying to NASA ethics officials investigating the matter.
Stadd faces up to 15 years in prison if convicted on all three charges.
NASA officials on Friday declined to comment on the indictment.
Stadd, who joined NASA as chief of staff in 2001 and left the agency in 2003, was President George W. Bush's NASA transition chief in 2000. Stadd "was centrally involved in the organization and management of NASA," said John Logsdon, a Smithsonian Institution space scholar.
"He was in many ways the White House representative to the NASA front office," said Logsdon, a member of the NASA Advisory Council. "So he had a fair degree of influence."
When Stadd announced that he was leaving, then-NASA chief Sean O'Keefe said, "Courtney has been a faithful public servant and a creative leader who knows how to motivate people and get things done."
According to the indictment, Stadd started a management consulting firm called Capital Solutions that specialized in advising aerospace-related clients, including Mississippi State University's Georesources Institute.
The institute paid Stadd $85,000 in fees and travel costs to provide technical document editing and prepare community outreach and public communications material, the indictment says.
Stadd returned to NASA as a special government employee in the NASA administrator's office for three months in 2005, the same year Congress had appropriated $15 million for NASA's earth science program.
The indictment accuses Stadd of using his position in the administrator's office to steer $12 million of the funds to Mississippi, and Mississippi State ended up getting $9.6 million of the funds through five subcontracts.