They could face up to 10 years in prison and a $250,000 fine.
However, an amnesty has now been offered until Friday evening for anyone else who hands over shuttle parts.
SHUTTLE BREAK-UP
Authorities have been searching for debris which could give them vital clues as to why the shuttle broke apart as it re-entered the Earth's atmosphere.
The two suspects were arrested in separate incidents.
Merrie Hipp, 43, was charged with stealing a shuttle circuit board from the wreckage.
Bradley Justin Gaudet, 23, was charged with stealing a scrap of thermal insulating fabric. They pleaded innocent and were set free.
"The issue here is the thermodynamics of the space shuttle and any piece of that is important to this investigation. No-one knows which piece will unravel the mystery," US Attorney Michael Shelby said.
US authorities have said they are conducting at least 17 investigations into reports of people taking shuttle debris as souvenirs.
'Missing link'
Nasa has moved away from the theory that insulation foam seen to peel away from Columbia's external tank on launch and hit the vehicle's left wing was responsible for the disaster.
"So we're looking somewhere else: was there another event that escaped detection? We're focusing our attention on what we didn't see," said Ron Dittemore, Nasa's space shuttle program manager.
"We're trying to find the missing link."
Nasa is particularly interested in finding parts of the left wing as, in the seconds before it broke up, Columbia tried to compensate for increased drag on its left, firing steering jets to right itself.
"It was doing well, but it lost the battle," said Mr Dittemore.
On Wednesday, Columbia's nose cone was recovered from an East Texas forest, where it had been discovered on Monday.
More than 12,000 remnants, many as small as coins, have so far been recovered.