WASHINGTON—A federal jury Wednesday convicted four former Blackwater USA private security guards in the shooting deaths of 14 Iraqis in a Baghdad traffic circle in 2007, closing a chapter in a saga that complicated U.S.-Iraq relations.

The guards were convicted on nearly every one of the 32 charges they faced. Nicholas Slatten, a sniper who prosecutors said started the shooting, was convicted of murder. Paul Slough, Evan Liberty and Dustin Heard were convicted on charges of voluntary manslaughter, attempting to commit voluntary...