The Department for Digital, Culture, Media & Sport (DCMS) allotted the cash to Ms Arcuri, chief executive of Hacker House, after she applied for £273,000 in October 2018 under the Cyber Skills Immediate Impact Fund (CSIIF).
The report from the Government Internal Audit Agency (GIAA) comes after Ms Arcuri denied reports that she received favouritism during Mr Johnson's eight-year stint as London mayor.
The report said the Approvals Board had approved Hacker House Ltd's application, but for a reduced amount of £100,000, adding: "This review concludes that although the initial gateway questions were not considered for the 19 applications received, the rationale for considering all applications was not unreasonable.
"In respect of the grant award to Hacker House Ltd, the assessment of eligibility and subsequent award of a reduced value of £100,000, is considered appropriate."
In an interview on ITV's Good Morning Britain earlier this month, Ms Arcuri said of Mr Johnson: "Never once did I ask him for a favour. Never once did he write a letter of recommendation for me. He didn't know about my asking to go to trips."
While the GIAA concluded that the assessment of eligibility and subsequent reduced grant award to Hacker House Ltd was appropriate, it did "observe areas where questions on the grant application form would have benefited from being clearer".
Examples it gave were defining "limited trading history" and a breakdown of the roles of staff employed by the lead organisation.
Earlier this month, a City Hall investigation into Ms Arcuri and her relationship with Mr Johnson was paused following a request by the police watchdog.
Members of the London Assembly oversight committee were due to start an inquiry in relation to allegations the Prime Minister showed favouritism to the former model during his time as mayor of London by giving her £126,000 in public funding and privileged access to three foreign trade missions.
But at the start of the meeting, the committee chairman said it had received correspondence from the Independent Office for Police Conduct (IOPC) "asking us to pause our investigation".
Mr Johnson has complied with a request for evidence from the committee and members have so far agreed with a request from the Conservative Party leader's solicitors for the submitted papers to be kept confidential.
The former mayor has previously accused his "old friends" in the London Assembly of "barking up the wrong tree" with their investigation.