The shuttle touched down at the Naval Air Station Joint Reserve Base in Fort Worth on Sunday afternoon.
It is being ferried from California to Florida atop a modified 747 aircraft, known as a Shuttle Carrier Aircraft. It refueled at Amarillo's airport earlier in the day and arrived in Fort Worth at 2:15 p.m.
Discovery is expected to stay overnight at Barksdale Air Force Base in Shreveport, La. The shuttle should reach Kennedy Space Center in Florida on Monday.
But weather conditions could change the plan, NASA said Sunday.
"The main thing we are worried about is moisture in the air and rain or thunderstorms, because those little tiny raindrops going at a high speed, acts like a BB and can hit the tile and break the tile," said Stephanie Stilson, of NASA.
Discovery landed at Edwards Air Force Base in California on Sept. 11 after completing a two-week, 5.7-million mile mission to the international space station.