The announcement ends weeks of political turmoil that culminated with Sonia Gandhi’s refusal to take the post.
Ms Gandhi was by his side and they appeared at ease, laughing when reporters shouted questions at them.
A senior Congress leader said on condition of anonymity that Mr Singh would be sworn in Thursday or Saturday. Friday, he said, was an auspicious date on the Hindu calendar, but also the 13th anniversary of the assassination of Rajiv Gandhi, who was killed by Sri Lanka separatists, leaving Sonia Gandhi a widow.
On Wednesday, the communists acknowledged past differences with Mr Singh’s economic policies. But they stressed that their primary aim now is to have a secular government to replace outgoing Prime Minister Atal Bihari Vajpayee’s Hindu nationalists.