Samuel Little, 74, appeared almost cheerful as he was found guilty of crimes that will jail him for life without chance of parole.
He chatted with his lawyer and, asked by Superior Court Judge George Lomeli about a possible September 25 sentencing date, Little replied casually, "It's your discretion."
"Well, I need an answer," the judge said.
"Sure - you're welcome," Little responded.
Defence lawyer Michael Pentz did not speak to reporters after the 10-minute hearing on Tuesday.
Jurors deliberated for just two hours before convicting him of three counts of first-degree murder.
The women were found nude below the waist and had been dragged into debris-strewn alleys.
Prosecutors linked the former boxer to the killings through evidence recovered at the scenes, which they compared to his DNA profile in a criminal database.
In 2012, Los Angeles detectives found Little living in a shelter in Kentucky and arrested him.
Little's known victims were 41-year-old Carol Alford, whose body was found on July 13, 1987; 35-year-old Audrey Nelson, found on August 14, 1989; and 46-year-old Guadalupe Apodaca, found on September 3, 1989.
Apodaca's son, Tony Zanbrano, 50, said his own life had been blighted by his mother's death and a quarter-century of not knowing who had killed her.
During the trial, prosecutor Beth Silverman said Little was probably responsible for at least 40 killings since 1980.
Authorities in California, Florida, Kentucky, Missouri, Louisiana, Texas, Georgia, Mississippi and Ohio are looking for possible links.
"It's the end of an entire career of killing," she said after the verdict.
It was difficult to track down Little and required help from law enforcement agencies from all over the country, Los Angeles police robbery-homicide Detective Mitzi Roberts said.
Little's victims were easy targets because they were drug-users and prostitutes on the fringes of society, authorities said.
Little had already been arrested in connection with crimes in 24 states, mostly assault, burglary, armed robbery, shoplifting and drug violations. In 56 years, he served less than 10 years in prison, authorities said.