The complaints, received from Labour MP Trevor Mallard and others, related to donations to Mr Banks' campaign from internet multimillionaire Kim Dotcom and casino operator SkyCity and to free radio advertising his campaign received.
Referring to two $25,000 donations from Mr Dotcom and $15,690 of radio advertising, police said they had established Mr Banks personally solicited the donations, which were subsequently recorded as anonymous in the electoral return that he signed.
Police also established that SkyCity chief executive Nigel Morrison handed Mr Banks a cheque for $15,000 in a sealed envelope at a meeting on May 24, 2010.
However, the investigation found Mr Banks' campaign finance return was compiled by a campaign volunteer and Mr Banks sought and received confirmation that it was an accurate return of his expenses before signing and filing it, which was allthat was required under the Local Electoral Act.
Mr Banks yesterday said he and his team had "always maintained that our 2010 electoral affairs were conducted within the law, and we are glad that these matters can now be put behind us".
But the police findings that Mr Banks solicited the donations and received the SkyCity cheque appear to contradict his original statements on the issue.
On April 27, when asked about Mr Dotcom's donations, Mr Banks told the Herald: "I kept the finances of the campaign [at] arm's length.
"Others were involved in collecting money and talking to people."
Green co-leader Metiria Turei said "it appears Mr Banks told a lie while he was a minister in John Key's Government ... he did not tell the truth about his involvement in soliciting donations for his campaign".
In response to questions from her and other Opposition MPs, Mr Key "assured the House he believed the statements that John Banks had made and that was the reason he kept him on as minister despite the allegations and police inquiry", Ms Turei said.
"John Key now needs to review that decision."
Labour leader David Shearer said Mr Banks appeared to have got off on a technicality.
"This is a guy that's gone to a donor, asked for money and in one case received a cheque in his hand and then has turned around and said he can't remember receiving it.
"Police can't prove it but everyone in New Zealand knows what's going on here. John Key knows as well and should stand him down."