Robert Ellis, 60, who was also an Australian passport holder, was killed on instructions from his Indonesian wife, they said, with one suspected motive being money.
Residents found the decomposing body of Ellis, who had lived on Bali for several years, early yesterday dumped next to a paddy field, wrapped up in plastic and blankets.
The wife, Julaikah Noor Ellis, went to the police to report her husband missing soon after the body was found, but she was later detained and named a suspect in the case.
"After talking to her slowly and kindly for a while, she finally admitted it."
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She was in the house at the time of the killing but told police that she was in her room when it took place, he said.
The boyfriend of a housemaid had carried out the killing, police said. The maid had admitted it took place in Ellis's kitchen between Sunday evening and Monday morning, they said.
Ellis had been living in a villa in Sanur, and his body was found in a village to the north of the tourist area, far from any houses.
He was originally from Britain but had been living in Australia for a long time before moving to Bali, and was a dual national.
The news comes after the body of an American tourist was found stuffed in a suitcase outside a hotel on the island in August.
Bali, a pocket of Hinduism in Muslim-majority Indonesia, attracts millions of foreign visitors every year with its palm-fringed beaches and tropical climate.
While foreigners often fall foul of Indonesia's tough anti-drugs laws, which include the death penalty, grisly murders are rare.