Police said Collins Jumaisi, a 33-year-old man living near the quarry in Mukuru neighbourhood in the south of the capital, was arrested early on Monday.
The acting head of police, Douglas Kanja Kirocho, said nine bodies had been recovered so far from the quarry.
"It is crystallising that we are dealing with a serial killer, a psychopathic serial killer who has no respect for human life," said Amin Mohamed, the head of the Directorate of Criminal Investigations.
Jumaisi confessed that he lured and killed 42 women and dumped their remains at the quarry, Mohamed said.
The murders stretch back to 2022, starting with Jumaisi's wife, with the most recent on July 11, Mohamed said in the televised statement.
At Jumaisi's home, police said they found several mobile phones, identity cards, a machete they believed was used to cut up the victims, industrial rubber gloves, rolls of sellotape and a dozen nylon sacks similar to those in which the victims were found.
Huge crowds gathered to watch the remains, many of which were dismembered, being retrieved from the quarry over the weekend, with some engaging in running battles with police.
Many local residents have been angered by rumours that the bodies were linked to alleged abductions of young protesters by security forces during recent street demonstrations.
The police have so far given no indication that the remains found are anything to do with the protests.
A government spokesperson shared a police statement on X on Friday saying that the authorities were analysing samples to identify the deceased and that investigations were under way.
An activist with the Mukuru Community Justice Centre rights group said most of the remains were decomposed, indicating they had been there for some time.
Earlier this month President William Ruto said reports of abductions by state agents were regrettable and that any officers found responsible would be held to account. Kenya's police chief Japhet Koome resigned on Friday.
