"This nation will keep watch; we will make sure that the ancient impulse of anti-Semitism never finds a home in the modern world," Bush said on Saturday as he campaigned in the key battleground state of Florida.
The state's Jewish population is the third largest in the world after Israel and New York.
The state department had opposed the legislation, saying it was unnecessary as the department already compiles such information in its annual reports on human rights and religious freedom.
"Defending freedom also means disrupting the evil of anti-Semitism," Bush told thousands of cheering supporters in Sunrise packed into a sports arena usually used by the Florida Panthers professional ice hockey team.
"Today, I signed the Global Anti-Semitism Review Act of 2004. This law permits the government to keep a record of anti-Semitic acts throughout the world, and also a record of responses to those acts," he said.
Florida is the richest haul among the battleground states expected to decide the 2 November presidential election, with 27 electoral college votes out of the 270 needed to win.
The US will now monitor incidents
of attacks on Jews worldwide
Jewish voters are thought to favour Democrats historically, but the Bush campaign hopes that his strong support for Israel and aggressive outreach efforts could win a majority of Florida's sizeable Jewish community.
The state department had drawn fire for its position from Jewish groups - which wield significant political power especially during a presidential election year - and in September, more than 100 prominent Americans signed a letter to US Secretary of State Colin Powell saying that the stance was "wrong".
"The fight against anti-Semitism deserves specific, focused attention," said the letter which was signed by former Republican vice-presidential nominee Jack Kemp and ex-UN ambassador Jeane Kirkpatrick among others.
The bill, known as the Global Anti-Semitism Awareness Act, was introduced by California Democratic Representative Tom Lantos, the only Holocaust survivor in the US Congress, in response to recent acts of anti-Semitism in Europe and the Middle East.
Jewish groups have hailed the passage of the bill, which they said provided a new avenue to fight anti-Semitism.
Under the legislation, the state department will have to produce an annual report on anti-Semitism around the world and form a specific office headed by a special envoy to document anti-Semitic abuses and design strategies to combat them.
Powell's office had opposed the
legislation, calling it unnecessary
It requires the department to document acts of physical violence against Jews, their property, cemeteries and places of worship abroad, as well as local governments' responses to them and take note of instances of anti-Jewish propaganda and governments' readiness to promote unbiased school curricula.
By tradition, Bush, who signed the legislation on his official Air Force One jet on his way to Florida, will treat the law's requirements more like strong advice and guiding principles because of the separation of powers.