Police took the 49-year-old suspect into custody after the shooting.
Floyd County Sheriff John Hunt said the officers had faced "pure hell" when they arrived at the man's home.
Four other people were injured at the scene in Allen, a small town in a mountainous part of eastern Kentucky with a population of just 166.
The officers who died in the shooting late on Thursday have been named as Capt Ralph Frasure, Deputy William Petry and dog handler Jacob Chaffins.
K9 Drago, one of the dogs that Mr Chaffins handled, also died.
Capt Frasure had been with the Prestonsburg, Kentucky, Police Department for 39 years. The department said he had served "with honor and glory up until the last second".
The men ran into a barrage of gunfire from a rifle when they went to the house on Main Street shortly before 19:00 local time (midnight GMT).
The shooting continued for nearly three hours before suspect Lance Storz was taken into custody, having surrendered after negotiations involving members of his family.