"A great responsibility now lies ahead of you and I trust that under your leadership the people of Sikkim will see prosperity and progress. I particularly hope that you will strive to improve the lives of the less privileged people in the state," the Dalai Lama wrote in a letter to Tamang.
"During my visits to Sikkim over the years, the people of Sikkim have shown me affection and warm hospitality, which I very much appreciated. The kindness and enthusiasm with which I have been received vividly reminded me of the strong emotions I felt during my first visit in 1956."
The Tibetan spiritual leader acknowledged that last month marked the 60th anniversary of the Tibetan people's life in exile in India.
Noting that there is a sizable Tibetan community residing in Sikkim, he took the opportunity to express deep appreciation for the warm and friendly way in which Tibetans have been received.
Tamang's Sikkim Krantikari Morcha won an absolute majority in the Sikkim Assembly polls, ending the 25-year reign of former Chief Minister Pawan Chamling and his Sikkim Democractic Front in the Himalayan state.
On Sunday, the Dalai Lama had greeted Arunachal Pradesh Chief Minister Pema Khandu and Odisha Chief Minister Naveen Patnaik on their parties' victories in the Assembly elections in their states.
The Dalai Lama fled Tibet for India after a failed uprising against Chinese Communist rule in 1959.
( With inputs from IANS )