James Allen, 36, was arrested in south Leeds at 7.20am on Sunday and is being held on suspicion of murder in connection with the deaths of Colin Dunford in Middlesbrough and Julie Davison in Whitby.
Cleveland police and North Yorkshire police issued an urgent appeal to find Allen following the murders.
A Cleveland police spokeswoman said: "A 36-year-old man has been arrested in south Leeds at around 7.20am today on suspicion of murder in connection with both incidents and inquiries are ongoing.
"Cleveland police and North Yorkshire police would like to thank members of the public for their support in this matter."
A West Yorkshire police spokesman said Allen had been arrested on Crown Point Road after an off-duty officer saw a man fitting his description.
Assistant Chief Constable Mark Milsom said: "An off-duty officer travelling to work this morning saw a man fitting the description of James Allen on Crown Point Road in Leeds.
"They called for colleagues in support who arrived quickly and an arrest was made. We would like to thank all members of the community who have been contacting us to assist in this matter."
A murder investigation was launched after the death of 81-year-old Dunford, who was found dead at his terraced house in Leven Street, Middlesbrough, on Monday.
A postmortem examination on Dunford, who was last seen alive at 5pm last Sunday, showed he had suffered serious head injuries as a result of a significant assault. Detectives said there was no sign of forced entry at the house.
Davison, 50, who lived alone, was found dead by her sister at her rented flat in Church Square on Wednesday. She had also suffered serious head injuries, police said.
Allen, who is originally from Blackpool, is believed to have known Dunford when he lived next door to him in Leven Street about a year ago, but it is not thought Allen knew Davison.
Police linked the two deaths on Thursday and three forces joined the hunt for Allen, with more than 100 detectives working on the case, after sightings of the suspect were reported in Leeds on Friday.
On Saturday, police released CCTV images taken of Allen in Scarborough during the week. The pictures showed Allen in a cash exchange in the seaside town on Tuesday and Wednesday and in a sports shop on Wednesday.
