WASHINGTON—Congress passed the most far-reaching tax bill in a decade late Thursday, averting across-the-board tax increases, enacting new breaks for individuals and businesses and laying a marker for how Washington might work in an era of divided government.

The bill goes to the White House for President Barack Obama's signature after the House overcame persistent liberal opposition and passed it with an unexpectedly large bipartisan majority of 277-148. The measure passed the Senate earlier in the...