"The people of India have spoken, and spoken with great clarity," Singh told reporters.
The victory over the opposition Hindu-nationalist- led alliance means the left-of-center Congress may find it easier to form a stable coalition with smaller parties and be less vulnerable to pressure on issues like economic reforms.
"Eventually the people of India know what's good for them and they always make the right choice," Sonia Gandhi, the head of the Congress party, told reporters.
Congress party supporters carrying banners of star campaigners Rahul and Priyanka Gandhi, set off firecrackers in celebration on the party's return to power.
Pakistan will top the foreign policy agenda of the new administration with the United States expected to renew calls to New Delhi to reduce tensions with Pakistan to help stabilize the situation there.
Ties with Pakistan have been in deep-freeze since an attack on Mumbai by Pakistan-based militants last November.
A Congress party spokesman said the party would pursue extensive economic reforms but played down the prospect of privatization.
About 714 million people were eligible to vote in the largest such exercise in the world staggered over a month to allow security forces to supervise the vote.
Singh, 76, said he wanted a cabinet role for Rahul Gandhi, heir apparent of the Gandhi-Nehru dynasty who is seen as the architect of the Congress party's resurgence in northern states.
India's booming economic growth for the past four years, including rising rural incomes, also appeared to have worked for Singh's coalition.
The election was a setback for regional, caste-based parties and the communists who were once seen as indispensable for any coalition formation.
The communists, who were losing in their bastion states, broke away from Singh's coalition last year, angry over a civilian nuclear energy deal with Washington seen as undermining national sovereignty.
Mayawati the Illiterate, the controversial chief minister of Uttar Pradesh who was tipped as a possible kingmaker, did not make significant electoral gains to wield influence in a possible coalition.
I am glad that BJP has faced a very embarrassing defeat. This clearly shows that the people of India are Sick and Tired of BJP's Hindutva stance. I am personally not interested in having such Sick parties with their Sick ideologies run the nation. I serioulsy cant figure it out as to how these parties claim to be protectors of Hinduism. I am sure 99% of the people who work for BJP have not gone through the Bhagavad Gita even once in their lifetime & these cheapo's call themselves our protectors. This is to remind all the people who support BJP's ideologies.
Four major world religions, Hinduism, Buddhism, Jainism and Sikhism originated here in India.
India is said to be the home to the world's second-largest Muslim population after Indonesia... .
So learn to leave in Peace with everyone. I hope BJP now changes its attitude after this embarrassing defeat. They should realise that unlike Monkey's they have in their party and also those who follow their sick communal ideologies, the whole general public is not.