The shuttle flight - Nasa's first on American Independence Day - was the second since the Columbia space shuttle was brought down three and a half years ago by a chunk of insulation foam breaking off the fuel tank.
The foam problem resurfaced during last July's flight of Discovery and again on Monday, keeping the space agency debating safety until the eve of lift-off.
Discovery thundered away from its pad at 2:38pm (1838 GMT).
Commander Steven Lindsey, a fighter pilot, was at the controls and aiming to dock with the international space station in two days.
Before lift-off, Mike Leinbach, the launch director, said: "Discovery's ready, the weather's beautiful, America is ready to return the space shuttle to flight. So good luck and Godspeed, Discovery."
It was unclear for a while on Monday whether Discovery would fly.
A slice of foam, no bigger than a crust of bread, fell off an expansion joint on Discovery's external fuel tank after Sunday's delay. Shuttle managers concluded on Monday night after engineering analysis that the remaining foam on that part of the tank was solid.
Engineers said the piece - 3 inches (7.6 centimetres) long and weighing a tenth of an ounce - was too small to pose a threat even if it had come off during launch and hit the shuttle. Inspectors found no evidence of further damage.
Nasa made sure there was no excessive ice build-up at that spot; ice could be even more damaging than foam at lift-off.
Space shuttle Columbia exploded,
killing all crew members
A Nasa administrator said earlier: "You could mail 10 of these things with the cost of a single first-class stamp.
"We're talking about a very, very minor piece of foam here. ... This is not an issue."
The fallen foam added to the tension surrounding this mission.
Nasa's chief engineer and top-ranking safety official objected two weeks ago to launching Discovery on the 12-day station delivery mission, without first eliminating the lingering dangers from foam loss, considered probable and potentially catastrophic.
They were overruled by shuttle managers and, ultimately, by Griffin. He stressed the need to get on with building the half-done, long-overdue space station before the shuttles are retired in 2010.
Riding aboard Discovery is Thomas Reiter, a German astronaut who will move into the space station for a six-month stay. He carried a small German flag out to the launch pad.
Two astronauts, an American and a Russian, are already living on the station; Reiter will expand the size of the station crew to three for the first time since 2003. Staffing was cut after Columbia crashed because of the lack of shuttle supply flights.
Besides Lindsey and Reiter, Discovery's pilot is Mark Kelly. Also aboard are Michael Fossum and Piers Sellers, who will conduct at least two spacewalks at the station, and Lisa Nowak and Stephanie Wilson.