Brian Goodwin, 33, is charged with first-degree murder in the death of 22-year-old Lauren Steed.
It happened inside a home in the 100 block of Freedom Trail, in the community of Saddlebrook.
New Castle County detectives say Goodwin shot Steed at some point on Monday.
At 1:42 p.m. Tuesday, police say Goodwin called 911 to say he shot someone, and that he was still armed with a weapon.
Crisis negotiators and the SWAT team responded to the home. After talking with those negotiators, Goodwin emerged from the home at 3:54 p.m. and was arrested by SWAT officers.
Officers then searched the home and found Steed dead from a gunshot wound.
According to the arrest affidavit, Goodwin said he shot Steed with an AK-47 rifle that he removed from a closet while packing to move out of the home.
"After insisting that he accidentally fired the rifle as she handed it to him, Brian admitted that it was he who reached in the closet and grabbed the rifle. He said that when Lauren called him Rambo, he held the AK-47 to his side and fired two times in her direction," the affidavit read.
He allegedly told police he purchased the gun approximately a month ago from someone in the city of Wilmington. Goodwin is being held on $10,000 cash bail.
He is scheduled for a preliminary hearing on May 4th.