He said the swearing-in of the new ministers would take place tomorrow.
"The governor has invited me to form the government since I have the numbers", Sangma said.
Meghalaya threw up a fractured mandate yesterday with the Congress emerging as the largest party, marginally ahead of its rival, the National People's Party (NPP), an ally of the BJP at the Centre and in Manipur.
The Congress, which has been in power in the state for the last 10 years, won 21 seats out the 59 that went to polls last month. The party is 10 seats short of a simple majority.
After meeting the governor, he had said, "We met the governor and submitted a letter of support from 34 MLAs -- 19 of the NPP, six of the the United Democratic Party (UDP), four of the People's Democratic Front (PDF), two each of the Hill State People's Democratic Party (HSPDP) and the BJP and an Independent."
Conrad Sangma (40) is the youngest son of former Lok Sabha Speaker (L) P A Sangma who died in 2016. He was elected a Member of Parliament in a by-election from Tura constituency after his father's death.