Should he be confirmed, Daschle will also head the new White House Office of Health Reform with Jeanne Lambew, who in the past has worked with Daschle on investigating health policy, as deputy director.
"It is hard to overstate the urgency of their work," Obama said, adding that health insurance premiums had nearly doubled under George Bush, the current president, and that 45 million Americans have no insurance at all.
"This simply cannot continue. The runaway cost of health care is punishing families and businesses across our country. We are on an unsustainable course, and it has to change," he said.
Stephen Chu is known as a strong supporter of renewable energy technology and research.
Chu, who is director of the Lawrence Berkeley National Laboratory, won the Nobel prize for physics in 1997 for his work on the "development of methods to cool and trap atoms with laser light".
In his current role, his work has focused on climate change.
Environmental groups have said that Obama's apparent choice shows that the president-elect is keen to implement renewable energy technologies in an attempt to reduce carbon emissions.
"It's a great sign to see a scientist named as head of this very important department, because it sends a signal that the issues of climate change and energy go well beyond ideology," Keya Chatterjee, from the World Wildlife Fund, told Al Jazeera.
"Our hope is that his first task we be how as a society in the US can achieve a low-carbon economy ... at a pace that matches the urgency of the problem [of climate change]."
Obama will also confirm three experienced policy makers and regulators to important environmental jobs, the Washington Post and the Los Angeles Times reported.
He has chosen Carol Browner, the former administrator for the Environmental Protection Agency (EPA), to fill a position overseeing energy, environment and climate policies, the newspapers cited unnamed Democratic party officials as saying.
The president-elect will also name Lisa Jackson, former head of the New Jersey Department of Environmental Protection, to head the EPA.
Meanwhile, Nancy Sutley, a deputy mayor of Los Angeles for energy and environment, will head the White House Council on Environmental Quality, the newspapers said.
The three appointments are expected to be announced by Obama later this week.