Suspect Ramon Alberto Escobar, 47, was arrested Monday after an attack on a sleeping man in Santa Monica.
The attack was apparently carried out with a set of bolt cutters that were recovered at the scene, police said.
As Santa Monica detectives were investigating the crime scene Monday morning, a uniformed officer saw Escobar walking down the street and determined that he matched the description, and the unusual bow-legged gait, of the suspect in the prior attacks. He was questioned and arrested.
Detectives with Los Angeles and Santa Monica say they later developed additional evidence linking him to all seven of the attacks.
Police say he is also linked to the disappearance of his own aunt and uncle in Houston, with whom he was living at the time. He fled Houston and drove to Los Angeles on the I-10 shortly after being questioned in connection with that case last month, police said.
Los Angeles Police Department Capt. William Hayes said Escobar has a criminal record that includes five years spent in a Texas prison from 1995 to 2000 for burglary, as well as an arrest in 2017 for assault and in February 2018 for criminal trespass.
Hayes also described Escobar as a "previously deported felon" who was originally from El Salvador and had apparently applied for asylum. He said officials are still researching his exact status.
He said after police arrested Escobar on Monday, they recovered a baseball bat that was believed to have been used in two murders and one attempted murder in downtown LA. The bat was found in Escobar's vehicle, a black Honda CR-V.
When asked if Escobar could be called a suspected serial killer, Hayes said police are considering whether to use that term, noting that serial killer is usually defined as one with three or more victims.
"He's a violent predator," Hayes said. "He's preying on innocent people. In most cases our victims were asleep."
Los Angeles and Santa Monica police plan to present their evidence to the Los Angeles County District Attorney's Office on Wednesday for filing consideration.
Escobar is being held without bail.