The judge held off entering a conviction last Thursday until sentencing on August 1 because Banks' lawyer, David Jones QC, gave notice he wanted to apply for a discharge without conviction.
It is highly unlikely a by-election will be held in Epsom to fill his vacancy.
Because the vacancy falls within six months of a general election, a by-election can be avoided with the support of 75 per cent of the Parliament.
Prime Minister John Key said tonight: "Mr Banks' resignation was the right thing to do under the circumstances."
"Given the proximity of the resignation to the General Election on September 20, the Government intends to seek Parliament's support not to hold a by-election in the Epsom seat, and will be taking a motion to the House in the first sitting week back."
Labour leader David Cunliffe said Mr Banks' resignation was inevitable "but should have come a lot sooner".
He criticized Mr Key for having described Mr Banks as an "honest" man, after the verdict on Thursday.
"The public has a right to expect the highest standards of its elected officials. The Prime Minister has presided over a serious decline in those standards."
"This Government's mandate has rested on a man found guilty of a serious electoral offence; on Peter Dunne, stripped of his ministerial warrants after he lost the trust of the Prime Minister having allegedly leaked a classified GCSB report; and on a Maori Party cravenly propping up the Government."
Banks said he would write to Parliament's Speaker, David Carter, tomorrow advising him of his resignation from Friday.
"This timeframe allows a number of constituency, administrative and staffing matters in Epsom and Wellington to be dealt with over the next few days," he said.
"I have been privileged to serve the people of Epsom and New Zealand at both a local level and in Wellington."
Banks is a former National MP and minister and former Mayor of Auckland, who was beaten by Len Brown in 2010.
He joined Act in concert with former National leader Don Brash in 2011 after Dr Brash conducted a coup against Act leader and former Epsom MP Rodney Hide.
Banks became the leader of Act in 2011 when he was the only Act MP elected.
Banks stepped down from the Act leadership in December last year after he was committed for trial on the election donations issue and he announced his intention to retire at the 2011 election.
Dr Whyte was elected leader in February and David Seymour was selected to contest Epsom for Act.
Banks' resignation will not affect National's ability to lead the minority Government.
With 59 MPs in the 121-seat Parliament, National needs 61 votes to govern now and when the House is reduced to 120 MPs on Friday.
National has the support of three MPs in the Maori Party and one MP in United Future, still giving it a comfortable majority.
Justice Edwin Wylie found Mr Banks guilty of filing a false return in relation to two donations of $25,000 made by Kim Dotcom's Megastuff company which were signed off by Mr Banks as anonymous.
At sentencing on August 1 he could face a fine of up to $10,000 and a prison sentence of up to two years although Justice Wylie said he would also consider home detention, and an application for a discharge without conviction.
