Soon after lift-off, small pieces of insulating foam were seen to fall away from the tank, but officials said that was expected and had posed no danger.
There had been fears Tuesday's launch would be delayed after a small crack was found in the foam.
But the shuttle was given the all-clear and left its Florida launch pad right on schedule at 1438 EDT (1838 GMT).
"The tank performed very, very well indeed," shuttle programme manager Wayne Hale said.
"We saw nothing that gives us any kind of concern about the health of the crew or the vehicle."
Some three minutes after take-off from the Kennedy Space Center, about six pieces of foam were seen to fall from the orbiter.
But Mr Hale said Discovery had been so high when the pieces came off, there was not enough air to accelerate them into the orbiter and damage it.
"It's all very minor. It's all very late... So at the end of the day, I'm very pleased with the performance of the tank. This is a great improvement from where we were," he said.
The flight is the first of 2006 and only the second since the loss of the Columbia orbiter three years ago.
The BBC's James Coomarasamy in Florida says that with a successful launch behind them, Nasa officials are putting up a united front in the face of unprecedented public disagreement about whether or not they needed more time for repairs before the launch.
Tuesday's successful blast-off followed a frustrating weekend when stormy weather over Kennedy had scrubbed two attempted getaways.
There were concerns the discovery of the small breakage in the fuel tank's insulating foam on Monday would lead to a further delay being ordered.
But Nasa said the defect posed no risk and cleared Discovery for launch.
The orbiter's seven astronauts - five men and two women - are making the 115th flight of the American shuttle programme.
Their mission will take them to the International Space Station (ISS).
They are delivering almost 13 tonnes of equipment and supplies to the ISS. One of their number - German Thomas Reiter - will be staying aboard the orbiting platform when the others leave in just under two weeks.
In addition to servicing the ISS, the mission will test safety systems introduced following the destruction of Discovery's sister ship Columbia and the deaths of its crew in February 2003.
Columbia was struck on launch by a large piece of insulation foam that punctured a hole in its left wing and left it open to the destructive superheated gases of re-entry.
Nasa has redesigned the tank to try to minimise foam loss but admits some breakaway is inevitable whenever a shuttle makes the eight-and-a-half-minute ascent to orbit.
When the vehicle nears the space station on Thursday, it will perform a back flip so that the ISS crew can inspect further the shuttle's heat-resistant surfaces, particularly on its belly.
Discovery is due to return to the Kennedy Space Center on 16 July.
(Sources: BBC, Reuters)