On the occasion, a dome-shaped monument - named "Arch for Arch" - was also unveiled at the Anglican St George's Cathedral in Cape Town in the honour of the Archbishop's freedom struggle.
The monument, constructed from 14 pieces of wood by Croatian boat builder Dario Farcic, has the excerpts from South Africa's Constitution inscribed in it.
In a special video message, the Tibetan spiritual guru also a Nobel Laureate, said that Tutu had impacted millions of people's minds to deeper human values, including faith.
The 82-year-old Dharamshala-based Tibetan spiritual leader also said that in this world, a lot of troubles and a lot of problems are our own creation.
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"The only remedy to these problems is compassion, forgiveness, love and tolerance. You always teach these values and you yourself practise and implement these things. Through your own word and actions, you show the real value of these things.
The Dalai Lama, who has been refused a visa by the South African government previously, also apologised for cancelling his visit to neighbouring Botswana due to his ill health.
"I hope to meet the President of Botswana and you on another occasion," he said.
In his brief address, thanking people who had joined him on his birthday, Tutu recalled how "the big march" against the apartheid regime started with 30,000 at the same Anglican St George's Cathedral, where his birthday was being celebrated.
"You were also instrumental in bringing down apartheid in South Africa. Post-apartheid, you have given such an important contribution to restoring justice and giving the victims a voice," the Institute said.
It was referring to Tutu's chairing of the Truth and Reconciliation Commission which Nelson Mandela had instituted after he became South Africa's first democratically-elected President.
Apart from the Dalai Lama and the Norwegian Nobel Institute, U2 singer Bono also read a poem in Tutu's honour through a video from Mexico, which has bestowed on the Archbishop "the Order of the Aztec Eagle", the highest decoration awarded to foreigners, to honour his humanitarian work across the globe.