The foundation stone of the monastery was laid by former CM Dorjee Khandu in 2007.
The ceremony was conducted in the presence of Governor PB Acharya, his wife, Chief Minister Pema Khandu, state Assembly Speaker T N Thongdok, Chief Secretary Shakuntala Gamlin and other dignitaries.
Thousands of devotees clad in yellow robes thronged the venue to witness the consecration ceremony by their living god.
"I was destined to be here for this momentous occasion. It is more important to be a good human being than a mere Buddhist or adherent to any faith," the Dalai Lama said in his address.