WASHINGTON—The House of Representatives passed a bill that would usher in the most far-reaching overhaul of the U.S. tax system in 31 years, a plan that would reduce the corporate tax rate to its lowest point since 1939 and cut individual taxes for most households in 2018.

The bill would repeal the alternative minimum tax, increase the child tax credit, abolish the estate tax by 2025 and transform the U.S. system for taxing multinational corporations. The plan also would raise taxes on some people by removing personal exemptions...