WASHINGTON—Congress gave final approval Wednesday to a $1.5 trillion tax cut, delivering a major victory for President Donald Trump and GOP leaders after nearly a year in political control of the capital.

At the heart of the plan—the most sweeping since 1986—is a cut in the corporate tax rate to 21% from 35% that is expected to provide a stimulus to the U.S. economy as soon as next year. The tax plan also cuts individual tax rates and aims to simplify the tax code by eliminating some deductions, trimming others, and jettisoning...