After the House of Representatives passed the bill by 257 votes to 167, Mr Obama said the measures were “just one step in the broader effort to strengthen the economy”.
It raises taxes for the wealthy and delays spending cuts for two months.
There had been intense pressure for the vote to be passed before financial markets reopened on Wednesday.
Financial markets have responded positively to the move.
In Asia, Hong Kong’s Hang Seng index opened up 2.1% on Wednesday morning, while South Korea’s Kospi added 1.7% and Australia’s ASX 200 rose 1.2%.
UK shares jumped 1.5% on opening, German stocks gained by 1.6%, while France’s Cac 40 rose 1.4% and Italy’s stocks gained 2%.
In Tuesday night’s house vote, 172 Democrats and 85 Republicans voted in favour of the bill.
A majority of Republicans, 151 in total, voted no, along with 16 Democrats.
The bill had been passed in the Senate less than 24 hours earlier by 89 votes to eight after lengthy talks between Vice-President Joe Biden and Senate Republicans.
Speaking before returning to Hawaii for his interrupted Christmas holiday, Mr Obama said that in signing the law, he was fulfilling a campaign pledge.
“I will sign a law that raises taxes on the wealthiest 2% of Americans… while preventing a middle-class tax hike,” he told a White House press conference.