Michael Aaron Pang was taken in by Italian authorities after he allegedly struck the elderly shopkeeper repeatedly in the head with a stool.
Reuters says the body of Norveo Fedeli was found at his clothing store in Viterbo on Friday.
After the incident, police looked at video surveillance, which showed a young man wearing sunglasses and a baseball cap leaving the store. They tracked the suspect to the nearby town of Capodimonte and within 24 hours, arrested him at a local bed and breakfast.
Pang and Fedeli allegedly scuffled before the incident, according to Italian police.
After the killing, they say Pang changed his outfit and took the elderly man's wallet before escaping the store with one of his shoes concealed due to blood stains.
At the bed and breakfast, police say they found the stolen wallet and evidence linking Pang to the murder of Fedeli.
Leading up to the killing, AP says Pang came into Fedeli's store twice to pick up $670 worth of designer clothes he ordered, but his credit card was declined.
Pang, a graphic designer from Kansas City, had been living in Italy for about two months, according to Italian police. He was born in South Korea.
He faces murder and robbery charges and is expected to appear in court on Monday.