The shuttle was reported to have entered orbit above the Earth.
The launch had been postponed once due to poor weather, and there were early concerns that high winds could again delay takeoff before the winds calmed.
The seven-member crew is led by commander Mark Polansky, who is joined by pilot William Oefelein, Nicholas Patrick, Robert Curbeam, Christer Fuglesang, and Joan Higginbotham.
The astronauts on the shuttle and support teams at mission control ran a series of tests in the first hours after liftoff to make sure the shuttle was functioning properly.
NASA had banned nighttime flights after the space shuttle "Columbia" disintegrated while returning to Earth in 2003, killing all seven astronauts aboard.
Damage to the heat shield of the "Columbia" during that launch caused it to break apart as it entered the atmosphere. NASA hoped that daytime launches would allow cameras more easily to spot any debris from the shuttle during liftoff.
Improvements to the tank, radar, and other systems monitoring for such debris led NASA to conclude that nighttime launches were safe again.
Launch integration manager Leroy Cain told reporters today that so far, everything is performing as it should.
"I spoke to our colleagues in mission control before coming in here, and they had absolutely no problems, not even a single fault summary message going uphill, no indications of any faults or problems on board the vehicle," Cain said.
NASA launch director Mike Leinbach also sounded pleased with the takeoff and performance of the shuttle.
"It all just came together perfectly," Leinbach said. "The countdown itself, there were just very few problems, just nips, nothing I could even talk about. It was so clean."
As the shuttle entered orbit above the Earth, commander Polansky told mission control back on the ground, "You've got a lot of smiling faces up here."
"Discovery" and its crew will be in space for 12 days. The shuttle is expected to dock at the International Space Station on December 11. The crew is expected to rewire the space station's power system to permit the installation of new laboratory modules.
NASA is seeking to help finish construction of the space station before the shuttle fleet is retired in 2010.