The measure passed by 63 votes to 37, falling short of the two-thirds majority needed to override the veto.
Opinion polls suggest most Americans back the research, which scientists hope will lead to cures for illnesses like Parkinson's and Alzheimer's.
But Mr Bush has consistently opposed embryonic research on moral grounds.
The vote came at the end of two days of emotional debates on three separate stem cell bills.
The most controversial bill, the Stem Cell Research Enhancement Act, scraps limits on federal funding imposed by Mr Bush in 2001.
It has already been passed by the House of Representatives.
The bill was backed by 44 Democrats and 19 Republicans, while 36 Republicans and one Democrat opposed it.
White House spokesman Tony Snow said Mr Bush's veto - his first in nearly six years in office - would be "pretty swift".
"He is fulfilling a promise that he has long made and he is keeping it," he said.
The other two - less controversial - bills received unanimous backing from the Senate, and are expected to be signed into law by President Bush.
One encourages stem cell research using cells from sources other than embryos, and the other bill bans the growing and aborting of foetuses for research.
In the years since Mr Bush imposed limits on federal funding, pressure has been building for a loosening of restrictions.
Opinion polls suggest almost two-thirds of Americans support the research.
Campaigners for stem cell research include prominent Republicans such as Nancy Reagan, whose husband, former President Ronald Reagan, died after a long battle with Alzheimer's.
But Mr Bush - along with many other conservative Republicans - has remained firmly against any change to the law.
"The simple answer is he thinks murder's wrong," Tony Snow said.
"The president is not going to get on the slippery slope of taking something living and making it dead for the purposes of scientific research."
It seems set to become an issue in November's mid-term congressional elections.Last Mod: 20 Eylül 2018, 18:16