Members of the public have been warned not to approach Cohen, who has mental health issues including paranoid schizophrenia.
Detective Inspector Ian Lott from the Homicide and Major Crime Command called the murder "a devastating attack on two women in their homes".
The women, aged 66 and 33, were found with stab wounds at their home in Golders Green Friday night and declared dead at the scene, according to the Daily Mail.
The suspect, who was known to the two victims, was arrested shortly before 2pm and was taken to a north London police station, police said.
He was last seen wearing a red Nike sweatshirt with a white logo on it. He is described as white male, 5ft 9ins tall, with short cropped hair and a short beard/stubble.
No arrests have been made.
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He was also wearing white trainers and dark grey pants or tracksuit bottoms. Any sightings of Joshua Cohen should be reported to police immediately via 999'.
Detectives added that he had recently shaved off his hair and eyebrows.
"The individual we are seeking was known to them and from all the information we have, acted alone".
In a press release on Saturday 12 August, the Met police confirmed next-of-kin have been informed of the deaths.
Det Ch Supt Simon Rose from Barnet added that he wanted to reassure residents that officers were doing everything they could to find him. "High-visibility foot patrols have been stepped up in the area and police will be on hand to listen and respond to community concerns".