Media reports said Singh, known as the father of India's economic reforms for launching the nation on the road to liberalisation when he served as finance minister in the early 1990s, would keep the finance portfolio.
The foreign minister's job in the communist-backed Congress government is expected to go to Natwar Singh, one of the 67 ministers sworn in by President Abdul Kalam at the sprawling presidential palace.
Natwar Singh, 73, served as envoy to various nations including Pakistan before joining politics. He will be a main driver of a nascent peace process with Pakistan.
Natwar Singh has said Congress was "willing to discuss everything from the nuclear issue to Kashmir" and would urge Islamabad to look at New Delhi's ties with China, with which it also has a border dispute but co-operates in other areas.
But he may take a harsher tack toward the United States.
Congress sources said he was a key figure in drafting Congress's election manifesto, which accused the previous Hindu nationalist government of creating a situation in which a "great country like India" had a subordinate relationship with the United States.
Also in the cabinet is another prominent Congress leader, Pranab Mukherjee, a former lawyer and journalist who may become trade minister.
Mukherjee, a graduate from Calcutta University, held the posts of commerce and finance in previous Congress governments and has three decades of political experience under his belt.
"Our priority will be to provide good governance in all aspects," said Mukherjee, 67, who has served on the boards of the international agencies such as the World Bank and the Asian Development Bank.
Another Congress leader Arjun Singh, 73, was mentioned as a contender for the home or human resources development ministries.
A long-time confidante of Congress president, Sonia Gandhi who walked away from the post of prime minister, Arjun Singh has served as commerce minister and human resources minister in the past.
Another familiar figure was Sharad Pawar, 63, a former defence minister who was tipped to take over either that portfolio again or the agriculture ministry - of vital importance in the still mainly farm-dependent economy.
Analysts say it was rural voters, angered at being left out of India's economic boom, who were responsible for the surprise upset of the ruling Hindu nationalists, whose "India Shining" campaign highlighting strong growth had flopped.
The lone woman of cabinet rank was Meira Kumar, daughter of a former defence minister Jagjivan Ram. Six other women got junior portfolios.
Manmohan Singh's government also included seven Muslim ministers, two of them with cabinet rank.
Maverick regional politician, Laloo Prasad Yadav, a key ally of Congress in the eastern Bihar state, was tipped to get the important railways portfolio. The rail network is the backbone of transportation in India where most people still travel long distances by train rather than road or air.
"The Congress-led alliance is a concrete formation and will last its five year term. Now the BJP should go to sleep and pack its luggage for ever," Yadav said.
Congress, which dominated India's first half century of independence, has been out of power since 1996. It has just 145 of the 543 elected seats, and its allies have 170.
It is being backed by the communists who support it from outside parliament.