WASHINGTON — The Senate on Wednesday gave final approval to legislation granting President Obama enhanced power to negotiate major trade agreements with Asia and Europe, sending the president’s biggest end-of-term legislative priority to the White House for his signature.

Senators then approved a bill that provides assistance to workers displaced by international trade accords, attaching it to a popular African trade measure that will go to the House for a final vote Thursday morning. House Democrats signaled they would support the measure, which they had voted down two weeks before.

The burst of legislative action secured a hard-fought victory for Mr. Obama and the Republican congressional leadership. It kept on track an ambitious agenda to complete a broad trade agreement joining 12 countries — from Canada and Chile to Australia and Japan — into a web of rules governing trans-Pacific commerce. Negotiators will also move forward on an accord with Europe, knowing that any agreement over the next six years will be subject to a straight up-or-down vote, but cannot be amended or filibustered in Congress.

The Senate cleared the so-called trade promotion bill 60 to 38, with 13 Democrats joining all but five Republicans. After the Senate voted 76 to 22 to cut off debate on the worker aid and African trade bill, senators agreed to pass it by voice vote.