The Transportation Security Administration said Tuesday it would soon allow fliers to carry certain smaller knives onto airplanes, one of the biggest moves to scale back the stringent airport-security measures established after the Sept. 11, 2001, terror attacks.

Beginning April 25, the TSA will allow fliers to bring knives aboard with blades no longer than 2.36 inches and no wider than half an inch. The permitted knives—which can't have molded handles, fixed blades or blades that lock in place—are similar to Swiss Army-style...