A whistleblower claimed that Vote Leave, the main campaign group advocating Brexit, sought to avoid a legal cap on spending by diverting funds to a smaller group to which it had close ties.
Coordination between supposedly independent campaigns is not allowed under electoral law.
Johnson condemned the claims, reported by the Observer newspaper and Channel 4 News, as "utterly ludicrous".
"#VoteLeave won fair & square -- and legally. We are leaving the EU in a year," he wrote on Twitter.
Vote Leave was close to the £7-million (8-million-euro, $9.9-million) legal spending limit when it donated £625,000 in the final days of the referendum campaign to a smaller pro-Brexit group, BeLeave, the reports said.
Shahmir Sanni, who worked on the BeLeave campaign, claimed that Vote Leave was heavily involved with the group's work, and "in effect they used BeLeave to over-spend, and not just by a small amount".
"They say that it wasn't coordinated, but it was. And so the idea that... the campaign was legitimate is false," he told Channel 4 News.
Vote Leave has denied this and a spokesman said it had "twice been cleared on this matter by the Electoral Commission".
An Electoral Commission spokeswoman said: "The commission has a number of investigations open in relation to campaigners at the EU referendum; it does not comment on live investigations."
In a further twist, Sanni reportedly accused a senior Vote Leave figure, Stephen Parkinson -- who is now Prime Minister Theresa May's political secretary -- of having "outed" him in his response to the story.
Parkinson was in a relationship with Sanni at the time and earlier said that any advice he gave was in that context. He later said he was "saddened" at Sanni's "factually incorrect and misleading" response.
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