Abdullah met Sonia Gandhi, the leader of the Congress party, on Tuesday to formalise the formation of the coalition.
The People's Democratic Party will provide the main opposition with 21 seats.
The elections saw a high voter turnout - more than 60 per cent - despite boycott calls by separatists who said the election would strengthen India's hold on the region.
Voting was largely peaceful, though there were scattered anti-India protests throughout.
Abdullah, 38, will be the third generation of his family to hold the post of chief minister. He inherited the National Conference leadership in 2002 from Farooq, his father. Sheikh Abdullah, his grandfather, was the region's most infuential leader in his lifetime.
Mirwaiz Omar Farooq, a key separatist leader, dismissed the new coalition as a shuffle of the same faces and ideologies.
"What is to be seen is whether this government will muster courage and represent the aspirations of people here,'' he said.
"What we need is a policy change in Kashmir, not an administrative change.''
The elections ended nearly six months of direct rule by New Delhi, after the previous chief minister resigned in August, following weeks of protests that left more than 50 people dead.
The Kashmir region is divided into Indian and Pakistan-controlled sections and the both countries claim it in its entirety.
Separatist groups have been fighting since 1989 to end Indian rule.