WASHINGTON -- The House of Representatives, in a display of anti-Wall Street sentiment, passed sweeping legislation Friday that rewrites the rules governing financial markets, aiming to restrict the operations of big banks and the powers of the Federal Reserve.

The legislation, if enacted, would bring the biggest change to financial rules since the 1930s, changing business practices for everyone from mortgage brokers in California to traders on Wall Street. The vote advances a major White House initiative designed to tackle...