Akong Rinpoche was stabbed to death, along with his nephew and driver, in the Chinese city of Chengdu in 2013.
State-run Chinese News Service said a third man was sentenced to three years in jail for his part in the killing.
Akong fled Tibet in 1959, later taking UK citizenship, and founded his monastery at Eskdalemuir in 1967.
The Chinese News Service said a court in Chengdu sentenced two men, named as Tudeng Gusang and Tsering Banjue, to death for the murders of the three men.
It cited authorities as saying that Gusang, who had worked at the Scottish monastery, and Banjue had stabbed Akong, his nephew and a driver to death in a dispute over a 2.7 million yuan (Â£284,000) payment.
The verdict, posted by the court on social media, said the murders were "brutal" and that the suspects would be "treated severely in accordance with the law".
The Samye Ling Buddist Centre was the first Buddhist monastery to be founded in Europe. Students later included David Bowie and Leonard Cohen.
Akong was born in Tibet in 1939 and quickly identified as the reincarnation of the abbot of the monastery Dolma Lhakang, in the eastern part of the region.
He was enthroned in the monastery at just four years old and then began his spiritual education. In 1959,  after the failed Tibetan uprising,  he fled to India. A few years later he moved to Britain.
Tudeng Gusang is believed to have worked at Samye Ling for five years making statues and believed he was owed money.
At the time of Akong's death, the monastery said the abbot had died defending funds that he was distributing in China.
Two men have been sentenced to death in China for the murder of the co-founder of the Samye Ling Buddhist centre in Dumfriesshire.