The former nationalist leader dramatically revealed he had resigned his membership of the party on Wednesday evening amid allegations of sexual harassment.
At the same time he announced a crowdfunding campaign to help with his costs in a legal action against the Scottish Government.
He is challenging the way the complaints against him have been handled - and also strongly denies the allegations.
By 8am on Thursday, his crowdfunder had raised more than £60,000 - exceeding the £50,000 target.
But opposition parties have attacked the fundraising move as “astonishing” and “unbelievable” - with some Labour politicians urging the public to donate cash to charities working with women who have suffered abuse instead.
Nicola Sturgeon, the current First Minister and SNP leader, voiced her “huge sadness” over Mr Salmond’s decision, but said she understood why her mentor for three decades had chosen to relinquish his party membership.
Mr Salmond made the revelation in a video message posted online on Wednesday evening.
He stated: “I have been a member of the Scottish National Party for 45 years, 20 of them as party leader and seven as first minister of Scotland.
“I hope I have done the party and the broader cause of independence some service.
“I truly love the SNP and the wider independence movement in Scotland. They have been the defining commitment of my life.
“But today I have written to the national secretary of the party resigning my membership.”
Mr Salmond said he was giving up his membership of the party he joined 45 years ago to avoid sparking internal divisions.
But he stressed his “absolute intention” to reapply for SNP membership “just as soon as I have had the opportunity to clear my name”.
Two complaints, fiercely denied by Mr Salmond, were raised in January against him and he was informed of an investigation in March.
The former SNP leader, who was Scotland’s longest serving first minister, is now taking court action against the Scottish Government, with papers lodged at the Court of Session in Edinburgh on Tuesday.
Ms Sturgeon had previously faced calls from opposition parties to suspend Mr Salmond from the SNP after the allegations emerged, but she insisted there was “no legal basis” to do so.
She also was clear that the complaints against her predecessor must be investigated and could not be “swept under the carpet”.
The allegations about Mr Salmond’s conduct towards two staff members in 2013, while he was in office, emerged last week.
Police Scotland confirmed on Friday that the complaints have been passed to the force.
Mr Salmond reiterated his strong denial of the allegations in the video message, saying: “Let me be clear again. I refute these two complaints of harassment and I absolutely reject any suggestion of criminality.”
Earlier this week, he wrote to Scotland’s top civil servant, calling for an inquiry into how the allegations against him were made public.
“In this case confidentiality has been broken greatly to my detriment and in a way which puts at serious risk the anonymity of both complainants,” Mr Salmond said in the message.
“It urgently needs to be established who breached that duty of confidence and why.”
He said his “entire focus” is now on preparing for the judicial review proceedings at Scotland’s highest civil court and he has launched a crowdfunder to help with costs.
A spokesman for the Scottish Conservatives said: “Scotland now faces the incredible and unprecedented situation of its most famous former first minister appealing to SNP supporters for cash to take legal action against the government he used to run.”
Scottish Labour MSP Rhoda Grant accused Mr Salmond of “dragging Scotland into the gutter”.