The bill passed Congress last week with rare bipartisan support.
The legislation creates tax breaks for companies that hire jobless veterans and helps them get job training and counseling.
"I urge every business owner out there who's hiring to hire a vet right away," Obama said. "They will make you proud, just as they've made this nation proud."
The bill also repeals a 2006 law that would require the federal, state and local governments to withhold 3 percent of their payments to contractors.
The veterans' legislation is the first proposal included in Obama's $447 billion jobs bill to win congressional approval.
The Associated Press contributed to this report.