An Electoral Commission investigation found pro-Brexit groups Vote Leave and BeLeave worked to a common plan, did not declare their joint working and did not adhere to the legal spending limits.
Evidence shows BeLeave spent more than £675,000 with Aggregate IQ under a common plan with Vote Leave, which should have been declared by Vote Leave, the commission said.
It means Vote Leave overspent by almost £500,000, with its spending limit set at £7million, the statement added.
Bob Posner, the Electoral Commission's director of political finance and regulation and legal counsel, said: "Vote Leave has resisted our investigation from the start, including contesting our right as the statutory regulator to open the investigation.
"It has refused to cooperate, refused our requests to put forward a representative for interview, and forced us to use our legal powers to compel it to provide evidence.
"Nevertheless, the evidence we have found is clear and substantial, and can now be seen in our report."
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Mr Posner added: "The Electoral Commission has followed the evidence and conducted a thorough investigation into spending and campaigning carried out by Vote Leave and BeLeave.
"These are serious breaches of the laws put in place by Parliament to ensure fairness and transparency at elections and referendums.
"Our findings relate primarily to the organisation which put itself forward as fit to be the designated campaigner for the 'leave' outcome."
Despite the investigation's findings, Brexiteers were given some good news yesterday.
Prime Minister Theresa May announced there will not be a second referendum into leaving the EU "under any circumstances".
A Vote Leave spokesman said the report contained "a number of false accusations and incorrect assertions that are wholly inaccurate and do not stand up to scrutiny".
He said: "Vote Leave has provided evidence to the Electoral Commission proving there was no wrongdoing. And yet, despite clear evidence of wrongdoing by the Remain campaign, the commission has chosen to ignore this and refused to launch an investigation.
"All this suggests that the supposedly impartial commission is motivated by a political agenda rather than uncovering the facts.
"The commission has failed to follow due process, and in doing so has based its conclusions on unfounded claims and conspiracy theories.
"We will consider the options available to us, but are confident that these findings will be overturned."