The European Union unveiled sweeping legislative proposals to raise taxes on big technology companies, a move that risks angering U.S. officials when trans-Atlantic relations are already strained by trade tensions.

The proposed taxes are among Europe’s most-aggressive measures to target the perceived excesses of a small cadre of tech superpowers, including Facebook Inc. and Alphabet Inc.’s Google, potentially adding hundreds of millions of euros to some tech firms’ tax bills. The U.S. warned last week against imposing tax...