Despite a boycott call by separatists, voter turnout exceeded 60 per cent, which many saw as an expression of Kashmiris' desire for better governance.
England-born Abdullah is heir to a political dynasty that has dominated Kashmir since India's independence and is the third member of his family to be elected to the troubled state's top post.
He is seen as a more popular choice than his father, Farooq Abdullah, who has faced criticism for his extravagant lifestyle, analysts say.
"I think the young generation of Kashmir is identifying itself with Omar [Abdullah], and if he also makes an effort to reach out to and identify with a violence-weary generation, he can deliver," said Bashir Manzer, a Kashmiri political analyst.
But others said unity cannot be achieved until he agrees to deal with separatist demands.
"[Abdullah] cannot ignore the recent massive freedom demonstrations. If he is sincere he should help address the aspirations of Kashmiris," said Mirwaiz Umar Farooq, chief of the region's main separatist alliance, All Parties Hurriyat [Freedom] Conference.
Sonia Gandhi, the Congress party chief, and her son Rahul, attended the swearing-in ceremony. The Congress is supporting Abdullah's new government.