The 51-year-old Golay was administered the oath of office by Governor Ganga Prasad at a function at Paljor Stadium on Monday.
He was elected as the leader of the SKM legislature party on Saturday night.
On Saturday, he had called on the Governor and staked claim to form the next government in Sikkim.
Prasad had reportedly told the SKM delegation to wait for his decision as he sought legal opinion on the matter as Golay had been convicted to a year's imprisonment in a corruption case in 2016 and had served the prison term, sources said.
After getting the legal opinion, the Governor invited Golay to form the next government, the Raj Bhavan source added.
The SKM, founded in 2013, won a slender majority in the 32-member Sikkim legislative assembly by bagging 17 seats against 15 won by the SDF.
Golay did not contest the assembly polls to devote all his time to campaign for his party.
(PTI inputs)