A review found there was a “close association” between the two and there may have been an “intimate relationship”, but there were no grounds for criminal investigation, the Independent Office for Police Conduct said.
The prime minister was accused of showing Ms Arcuri favouritism by giving her £126,000 in public funding and privileged access to foreign trade missions while he was in City Hall between 2008 and 2016.
The Independent Office for Police Conduct (IOPC) had been considering whether Mr Johnson should be investigated for the criminal offence of misconduct in public office.
Mr Johnson's spokesman said the review was a "waste of police time" and welcomed "the fact that this politically motivated complaint has been thrown out".
“Such vexatious claims of impropriety in office were untrue and unfounded," the spokesman added.
Len Duvall, the Greater London Authority’s (GLA) oversight committee chair, said: "The IOPC was looking specifically at whether he committed a criminal offence.
"That’s not our remit and their decision doesn’t have any real bearing on our investigation, which will focus on his conduct as mayor of London."
He added: “Our investigation will consider whether Boris Johnson conducted himself in a way that’s expected from anyone in that position."
Mr Johnson has always denied allegations against him and around the time allegations were first made, he said "everything was done in accordance with the code... and everything was done with full propriety".
Opponents of Mr Johnson say he should have declared an interest relating to his links with Ms Arcuri, after reports said the pair had an affair.
In September 2019 he told the BBC "there was no interest to declare," adding: "Let's be absolutely clear, I am very, very proud of everything that we did and certainly everything that I did as mayor of London."
In October the Government Internal Audit Agency ruled a £100,000 grant awarded to the former model, was "appropriate".
The IOPC said there is “no evidence” that Mr Johnson influenced the payment of sponsorship monies to Ms Arcuri or her firms.
It also found "no evidence" to show Mr Johnson “sought to influence, or played an active part in securing” Ms Arcuri’s participation in trade missions.
There is, however, "some evidence" that Mr Johnson may have been aware that Ms Arcuri was on an attendee list for a New York trade mission event, even though he disputed it.
Ms Arcuri has also denied being shown favouritism, claiming in October that she was "being used as collateral, all the allegations are false".
She added: "I had every right to be on those trips as a legitimate businesswoman and stand by everything that happened because these allegations are completely false.
“Someone has gone to great lengths to put together a massive attack and I stand by the legitimacy of my business.
“I am in fact a legitimate businesswoman.”
In an interview with LBC radio in October, the PM suggested stories about him and Ms Arcuri had come to light because of the government’s stance on Brexit.
“There are quite a lot of well-meaning and highly intelligent people who basically think that that would be something they don’t want to see, and I think that there is a concerted effort now to frustrate Brexit,” he said.
Mr Duval said: “Everyone who holds public office, whether you’re the mayor of London, or indeed the prime minister, is expected to adhere to the principles of public life – including integrity, selflessness, openness and honesty, to name a few."