Yes, broccoli is safe for cats and dogs to eat - just make sure it's in small quantities. As Dr. Chris Miller, a veterinarian at Atlas Vet in Washington, D.C., tells The Dodo, "Broccoli is often safely added to dogs' diets to increase fiber content and to help with increasing the volume of food while decreasing the overall calorie content."
As for felines? "Broccoli has not been known to cause problems in cats, but it may be troublesome to get them to eat it," Dr. Miller said. (Clearly, these cats disagree!)