West Midlands Police launched a manhunt for Anthony Russell, 38, after a mother and son were found dead in separate flats in Coventry earlier this week.
Another woman’s body was found on grassland in Leamington on Thursday and has been linked to the other two murders.
Julie Williams, 58, and David Williams, 32, were found dead on consecutive days. 31-year-old Nichola McGregor from Leamington was found around midday on Thursday.
Mr Russell, who has no fixed address but has links to Coventry, is also under suspicion of robbery, after police found him in a red Ford C-Max car, which was stolen in a car-jacking in Leamington on Wednesday afternoon.
The suspect was due to be questioned on Friday.
Assistant Chief Constable Mark Payne said: “The deaths of three people in the Midlands region this week have been shocking and devastating for the families involved. Our thoughts remain with them as they come to terms with the tragic circumstances of their deaths.
“We are grateful to everyone who has assisted with our appeals for information, but although we have a suspect in custody, our investigation must now establish exactly what has happened.”
A 36-year-old man has also been arrested on suspicion of conspiracy to commit murder, and has since been bailed with conditions.
West Midlands Police urge anyone with any information to contact the force. Members of the public can get in touch via Live Chat on west-midlands.police.uk between 8am and midnight, call 101 anytime or ring Crimestoppers anonymously on 0800 555 111.