President Donald Trump on Monday reinstated the ability of local police agencies to receive surplus military equipment, including grenade launchers and large-caliber weapons, reversing a ban that the Obama administration had implemented following protests over police tactics in Ferguson, Mo.

Attorney General Jeff Sessions, who has overturned a series of Obama-era directives that were opposed by many police departments, announced the change in a speech before the National Fraternal Order of Police, the nation’s largest police...