The space shuttle, Discovery, lifted off from Cape Caneral at 1637 BST after a 90-minute delay due to unsuitable weather conditions.
Half a million people in the streets around the Kennedy Space Center watched the take-off, which Nasa said went without a hitch.
The primary objective of the five-man crew commanded by Frederick Hauck is to launch a communications satellite - a replacement for one lost when Challenger exploded.
Tension
But the successful completion of the four-day mission is also crucial for the future of America's space programme and the nation's prestige.
The tension in the space centre's control room increased as the take-off was delayed after weather reports said winds in the upper atmosphere were too light.
But relief began to set in after the shuttle flight passed the psychological barrier of 73 seconds - the time after launch when Challenger was lost.
"I'm just glad to see us going again - it's important not only from a supply for the space station aspect but means we can get on doing the research we're supposed to," Senator John Glenn told the BBC.
US President Ronald Reagan - who watched the launch from the White House - announced he was delighted with the achievement.
"America is back in space! We're now looking forward to the successful completion of the Discovery mission and the safe return of her five-member crew," he said.
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