Sangma, 40, who is currently a Lok Sabha member from Tura, was administered the oath of office and secrecy by Prasad at the Raj Bhavan.
Apart from Sangma, 11 other cabinet ministers were also sworn in by the governor.
They are Prestone Tynsong, Comingone Ymbon, Sniawbhalang Dhar and Conrad's brother James P K Sangma (all from NPP), Metbah Lyngdoh, Lakhmen Rymbui, Kyrmen Shylla (all UDP), Banteidor Lyngdoh (PDF), Hamlet Dohling (PDF), Samlin Malngiang (HSPDP) and A L Hek (BJP).
Prime Minister Narendra Modi congratulated Sangma on becoming the chief minister.
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"Congratulations to @SangmaConrad on taking oath as Meghalaya CM. I also congratulate all others who were sworn in today. My best wishes to this team as it begins to work towards fulfilling the dreams and aspirations of the people of Meghalaya," he tweeted.
After the swearing-in ceremony, Sangma told reporters that his government is clear about its agenda which is good governance.
"I want to say that we as a cabinet, as a government and in fact all the MLAs and political parties will work together to take our state forward," he added.
Shah also took to Twitter to congratulate Sangma.
"Congratulations to the newly sworn in CM of Meghalaya Sri @SangmaConrad and his team. I am sure that the new government of Meghalaya under the central guidance of PM@narendramodi ji will act as a double engine to bring peace, progress and prosperity in the state of Meghalaya," Shah tweeted.
The Conrad Sangma government is supported by the United Democratic Party (6 MLAs), Peoples' Democratic Party (4), two MLAs each of the Hills State Peoples Democratic Party and the BJP and an Independent MLA Samuel Sangma.
First time UDP MLA Kyrmen Shylla, 26, became the youngest minister.
Meghalaya threw up a fractured mandate on Saturday with the Congress emerging the largest party winning 21 seats.
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