Members of the public who read the article then gave officers his name.
Damarey arrived in Auckland in July and went to Christchurch this month.
He is understood to have been living in a flat on the eastern side of the city.
Constable John Goddard, the officer in charge of the case in Auckland, spoke to Damarey last week.
At that stage, he was refusing to co-operate with the police.
However, he handed himself in to the New Brighton police station in Christchurch soon after.
"As a result of the pressure placed on Damarey with his name and picture being published as well as an appearance on not only the Herald website but also the police website, he felt he had no option but to hand himself in," Mr Goddard said.
"He has been charged with burglary and will be kept in overnight to appear in the Christchurch District Court.
"Immigration is now in the process of reviewing his visa."
Damarey is understood to have no criminal history in France.