The plane was left dangling from the building
The plane, a single engine Cessna, slammed into the Bank of America building around the 28th floor shortly after 1700 (2200 GMT), but no-one else was injured.
Meanwhile two other small planes have crashed elsewhere in America - one outside Los Angeles and another in Boulder, Colorado killing each of the pilots, White House spokesman Scott McClellan said.
"None of these incidents appear to be related and there's no indication of terrorism," he said.
President Bush has been briefed on the Tampa incident and Homeland Security Director Tom Ridge and the Federal Aviation Administration were notified.
Flying lesson
The teenage pilot in the Tampa crash has been named as Charles Bishop, from nearby Palm Harbor.
He was dropped off for a flying lesson by his grandmother at the St Petersburg-Clearwater airport, about 30 kilometres (20 miles) from Tampa, said Pinellas County Sheriff's spokesman, Greg Tita said.
Bishop took off alone when the instructor walked away after telling him to do a pre-flight check, Mr Tita said.
Bishop had been learning to fly for some time, but was not authorised to fly alone - the minimum age for a solo pilot in the US is 16.
Instructions ignored
The airport immediately notified the Coast Guard, which sent a helicopter to intercept the four-seater plane.
Coast Guard spokeswoman Lieutenant Charlotte Pittman said the helicopter attempted to give the pilot visual signals to land at a small airport, but the plane had failed to respond.
It was not yet known whether Bishop deliberately flew into the building or could not avoid hitting it.
"I saw a big cloud of smoke," said Eric Reyes who witnessed the crash. He said he saw one wing fall and hit the ground, followed moments later by the other wing.
Terror flashback
Following the crash the tail of the light aircraft could be seen dangling from the western side of the office building, which was nearly empty at the time.
Although on a completely different scale, the incident had echoes of the 11 September attacks in New York and Washington in which hijacked passenger planes were flown into the World Trade Center and Pentagon buildings.
One witness told local a television station that he was working on the 42nd floor at the top of the building with about 25 colleagues at the time of the crash.
He said they had heard a thud but were unaware of what had happened until he saw the police cars and helicopters.
"It brought back some very scary footage," he said, referring to the images of the 11 September attacks.