Detectives say 39-year-old Kori Ali Muhammad laughed as he recounted the shooting rampage, which includes gunning down a motel security guard on Thursday.
Now, police are saying the killings were completely random and the gunman wanted to kill "as many white people as possible".
Three people have been shot and killed in California by a gunman whom it is alleged had a dislike of white people and government.
Francine Williams described her 25-year-old son as a kind and giving person who had recently gotten engaged.
Dyer said his department had contacted the Federal Bureau of Investigation over the incident.
Muhammad told officers who arrested him that he was the man they were looking for, Mr Dyer said, saying: "I did it".
Muhammad watched police investigate that murder overnight from the rooftop of a nearby gas station.
The guard, Carl Williams, 25, was shot multiple times. The murder occurred last week, Dyer said.
Muhammad admitted the killings to officers as they arrested him, according to the chief.
Muhammad led investigators through the crime scene at the motel as well as the locations from Tuesday's shootings, Dyer said.More news: Kenyans take the honours in Boston Marathon
Muhammad hid out in a ravine and practiced voodoo rituals after the motel slaying.
Muhammad was in the area because of several abandoned houses in the vicinity; according to Dyer, Muhammad was living on the streets and was hoping to stay at one such house. Dyer played audio of the shots fired recorded by ShotSpotter during today's press conference.
After the shooting spree, police went over Muhammad's social media posts to find a motive.
Muhammad cut off his braids and shaved his face, significantly changing his appearance, after Fresno police put out a news release about that killing.
Police and witnesses said that in less than two minutes he fired 16 shots and gunned down and killed three White men. Dyer showed pictures of Randalls' family photos with his children after identifying him.
On Tuesday, police said, he acted on that hatred. It was unclear whether he had obtained an attorney.
The shootings happened outside a Catholic Charities building, but spokeswoman Teresa Dominguez told the Associated Press that the charity does not believe the suspect was tied to the nonprofit organization. They spoke. The man then took the gun from Muhammad and fled. Fresno's police chief said his former name was Cory McDonald.
Dyer said officers asked Muhammad why he chose to surrender. He is expected to be charged with four counts of murder and arraigned Friday.
Chief Jerry Dyer on Wednesday explained to members of the media a second-by-second breakdown of the rampage that left three men dead, including playing recordings of the gunshots captured on police tracking equipment. Mark James Gassett, a 37-year-old from Fresno, died in a neighborhood, and 58-year-old David Martin Jackson of Fresno was shot outside a charity office and died at a hospital.
On Tuesday, after he learned he was wanted for the guard's death, he set out to kill more people, Dyer said. "It looks like a guy carrying his groceries home from the store", Hughes said. Detectives believe it was picked up by a Hispanic man near the shooting scene.