The man handed himself into police on Saturday after his photo appeared in the Otago Daily Times and on social media.
He stole $420 from a New Zealand woman's hotel room in Dunedin on Valentine's Day after following her and a friend to the room after the pair won the cash at the casino, Detective Sergeant Steve Salton said.
The woman went to the bathroom and came out to find the man rummaging in her handbag.
He then fled.
She gave chase but failed to catch him.
She then discovered the money was missing from her handbag.
The American spoke to detectives yesterday.
"He denied everything, of course,'' Det Sgt Salton said.
"But I gave him the option of a pre-charge warning or going to court and he chose the pre-charge warning.''
The warning meant the man admitted the crime and had to make reparations to the woman.
"He just happened to have $420 in his wallet,'' Det Sgt Salton said.
Immigration New Zealand was assessing whether the man could remain in New Zealand.
The Valentine's Day incident was not the first to bring the American to police attention.
He had been barred from backpackers' accommodation in Christchurch, Queenstown and Dunedin, Det Sgt Salton said.
He advised the public to remain vigilant and be cautious if they encountered anyone fitting the American's description.
Anyone with information that can help should contact Dunedin police on 471-4800.
Information can also be provided anonymously to Crimestoppers on 0800 555-111.
