Fulfilling a campaign promise, Obama signed an executive order expected to set in motion increased research that supporters believe could uncover cures for serious ailments from diabetes to paralysis.
Bush issued a directive in 2001 banning federal funding for research into stem lines created after that date.
The decision limited the use of taxpayer money to only the 21 stem cell lines that had been produced before his decision.
Rob Reynolds, Al Jazeera's senior Washington correspondent, said that reversing unpopular Bush administration policies gave the new president positive political momentum.
"Stem cell research, while it is vociferously opposed by a certain segment of the population - religiously-oriented voters - is broadly popular among the majority of voters and the majority in congress," he said.
Bush was accused by scientists and politicians of injecting politics and religion into policy decisions on stem cells and other issues such as climate change, energy and contraception.
Obama promised a "new frontier" for science in the US - free from political ideology.
He directed the White House Office of Science and Technology Policy to ensure that "we base our public policies on the soundest science," and appoint scientific advisers based on expertise and "not their politics or ideology".
However, Obama said that "strict guidelines" would be developed for stem cell research and vowed not to permit human cloning, which he said "has no place in our society, or any society".
Dr Harold Varmus, a US Nobel Prize winning scientist serving as an adviser to the Obama administration, said the president would give the National Institutes of Health 120 days to come up with a framework to govern the use of federal funds to work with human embryonic stem cells.
"Hallelujah! This marks the end of a long and repressive chapter in scientific history."
Dr Robert Lanza,
chief scientific officer at Advanced Cell Technology
He said that Obama "in effect, is allowing federal funding on human embryonic stem cells research to the extent that is allowed by law".
Dr Robert Lanza, chief scientific officer at Advanced Cell Technology in Massachusetts, welcomed the changes.
"Hallelujah! This marks the end of a long and repressive chapter in scientific history. It's the stem cell 'emancipation proclamation'," he said.
Shares in biotech companies that focus on stem cell research soared after Obama gave his news conference, with those in Geron Inc leaping 23 per cent and StemCells Inc stocks rising 43 per cent.
Dr Douglas Melton, co-director of the Harvard Stem Cell Institute, noted that the process of getting federal funding itself is time consuming but said his group would seek the money, alongside its other sources of funding.
"The removal of this barrier that has stood in our way for eight years will open important new areas of research, and help in moving the field forward more rapidly," he said.
Stem cells are long-living cells that are the source of all other cells in the body.
When taken from days-old embryos they are virtually immortal and can give rise to all the other cells and tissues in the body.
Supporters say they can transform medicine and researchers have been working on using them to repair severed spinal cords, regenerate brain cells lost in cases of Parkinson's Disease and restore the tissue destroyed by juvenile diabetes.
|Researchers say stem cells could help treat ailments from diabetes to paralysis [File: AFP]
But opponents say the government crosses a moral line by supporting stem cell research and the government should not fund programmes that require the destruction of human embryos.
John Boehner, Republican leader in the House of Representatives, said Obama had undermined "protections for innocent life, further dividing our nation at a time when we need greater unity to tackle the challenges before us".
In his election campaign, Obama spelled out his policy on stem-cell research in a list of answers to the Science Debate 2008 scientific lobby group.
"I strongly support expanding research on stem cells," Obama wrote.
"I believe that the restrictions that President Bush has placed on funding of human embryonic stem-cell research have handcuffed our scientists and hindered our ability to compete with other nations."
Stem cell research is controversial internationally, with Britain, Belgium, Sweden, Canada and New Zealand actively encouraging embryonic stem-cell research, while Austria, Lithuania and Poland have laws restricting such research.