The American businesswoman, 35, made the admission in an interview with the Daily Mail following accusations last year that Mr Johnson gave her favourable treatment as mayor.
The Prime Minister avoided a criminal investigation after the police watchdog found no evidence he influenced the thousands of pounds of public money awarded to Ms Acuri or secured her place on foreign trade trips he led.
When asked whether she had an affair with the PM, Arcuri said: ‘I think that goes without saying. It’s pretty much out there… But I’m not going to talk about it.’
The pair first met at an event for venture capitalists in 2011 when Mr Johnson was married to lawyer Marina Wheeler.
He spoke at several of Ms Arcuri’s events free of charge and is said to have visited her Shoreditch home up to ten times.
The businesswoman told the Mail: ‘At the time I cared for him very deeply, but I never used the L word. I wouldn’t have recognised being in love.
‘There are romantic men and there are jesters of romance like Boris, and they’re not the same thing.’
It comes after a Boris Johnson biography, written by journalist Tom Bower, was published on Thursday.
Addressing the police watchdog conclusion in May, a spokesperson for the prime minister said: ‘We welcome the fact that this politically motivated complaint has been thrown out.
‘Such vexatious claims of impropriety in office were untrue and unfounded. “An independent review by the government Internal Audit Agency similarly showed the claims made by the Labour Party were false.
‘This was not a policing matter, and we consider this was a waste of police time.’
Get in touch with our news team by emailing us at [email protected].
For more stories like this, check our news page.