Dr Choje Akong Rinpoche set up the Samye Ling Tibetan centre in Dumfries and Galloway in 1967.
A statement from police in the Chinese city of Chengdu said Choje Akong Rinpoche, his nephew and his driver were killed in a residential area.
It said three suspects - all of whom were Tibetan - had stabbed the men to death in a dispute about money.
The Chinese police said: "The three suspects have confessed to the crime and the case is still under investigation."
A statement on the official website of Tibetan Buddhist leader the Karmapa Lama said he was "shocked" by the news and offered his condolences to his family members and everyone at the monastery.
"I hope that all of his visions and aspirations may continue to be fulfilled," he added.
A Tibetan monk who founded the first Buddhist monastery in the UK has been killed in south west China.