The Senate voted Wednesday to give President Barack Obama "fast track" authority to negotiate trade deals—one of the final steps in a long political battle that pitted the White House against House Democrats.

The bill—which passed 60-38 in the Senate—will be sent to the president's desk later this afternoon, but it was not immediately clear when he would sign it. Unions and most congressional Democrats say free-trade deals cost U.S. jobs and reward countries that pollute and mistreat workers. Obama and most Republican leaders say U.S. products must reach broader markets.

President Barack Obama. Getty Images

After killing one version of fast track (also known as Trade Promotion Authority, or TPA), the House eventually voted last week to pass the measure. The Senate plans to vote on three other trade-related bills. One would extend a job retraining program for workers displaced by international trade. That program requires House approval, too. Read MorePacific trade: Why DC is fighting about 'fast-track'

On Tuesday, Senators voted 60-37 to streamline the debate process—a key victory for the Obama-backed measure. Senate passage Wednesday of fast-track authority boosts Obama's hopes for a 12-nation Pacific-rim trade agreement. Members include Japan, Malaysia, Mexico and Canada.