The victim was identified only as an American man who was related to a coach on the U.S. men's volleyball team. An American woman, also part of the coach's family, was injured in the attack, along with a Chinese tour guide.
A Chinese man attacked them shortly after midday at the centuries-old, 45-metre-high (148-ft-high) Drum Tower in central Beijing. He died after leaping from the Tower after the attack.
Assaults on foreigners are rare in Beijing, host of the 2008 Olympic Games. Police said both the American woman and Chinese tour guide were out of danger, without elaborating.
"While at the Drum Tower in central Beijing, the two family members were stabbed during an attack by what local law enforcement authorities have indicated was a lone assailant. One of the family members was killed and the other seriously injured," the U.S. Olympic Committee said in a statement.
Tang Yongming, 47, from the eastern city of Hangzhou, leapt from the second storey of the Drum Tower after the assault, police said in a statement.
Local police said they did not know the motive for the attack.
International police organization Interpol said the attacker's name had not been found in any of its databases.
U.S. President George W. Bush, in Beijing for the start of the Games with his wife Laura, offered condolences and whatever assistance the victim's family needed.
"Our thoughts and prayers are with the victims and their families," he told reporters.
A U.S. embassy spokeswoman said earlier that diplomats had been dispatched to the Beijing hospital where the surviving tourist and the local tour guide were being treated.
"We're actively following the situation right now and U.S. Embassy officials are already at the hospital," the spokeswoman said.
Beijing has been calm in the run-up to the Summer Games, with security tight across the capital and thousands of security officials patrolling Games venues and streets.
A crowd had gathered around the ancient Drum Tower which had been closed off by police.
The U.S. volleyball team is due to play their opening game against Venezuela on Sunday.
