The plan extends for two years all Bush-era individual tax rates, prevents a spike in taxes on capital gains and dividends and renews long-term jobless insurance, while providing new tax relief for students, working families and businesses.
The drama now moves to the House of Representatives, where many of Obama's fellow Democrats strongly oppose the measure as favouring the wealthy and are still angry with him for cutting the deal with Republicans without them.
The House will start debate on the tax deal on Thursday, a senior Democratic aide said.
Most of the 255 House Democrats may oppose the package, but it is expected to be approved with overwhelming support among the chamber's 179 Republicans.
House Democrats are becoming more resigned to passage of the $858bn (£541bn) package, which is expected to boost economic growth next year but add to the budget deficit.
"At the end of the day I think we are going to have to pass a bill," said liberal Representative Henry Waxman.
Senate Republicans and Democrats backed it in a rare show of bipartisan support in the U.S. Congress.