Mr Wilson is understood to have made his decision after “increasing conflict” over the SNP’s defence policy including its position on Trident and membership of Nato.
In a draft letter addressed to the First Minister, which has been seen by The Scotsman, Mr Wilson said he had remained a member of the SNP for the duration of the referendum campaign to ensure that his resignation did not distract from the push for independence.
Mr Wilson, who was elected in 2007, said he was still committed to the concept of Scottish independence and hoped to continue to be part of the grassroots movement built up over the past two years, but not as a member of the SNP.
Yesterday, he cited the SNP’s decision to abandon its long-standing opposition to membership of Nato as a key reason for leaving the party.
Mr Wilson, an MSP for Central Scotland, said he would serve out his term at Holyrood as an independent and would decide whether to support the SNP in parliamentary votes on an “issue by issue” basis. He declined to say whether he would stand for election as an independent in 2016.
Last night, he told The Scotsman: “I’ve made a decision to go, to resign from the SNP and the SNP whip. It was in terms of policy about Nato. There was a divergence of policy. There were a lot of issues. Things were happening with local branches and complaints about the headquarters. It was about internal democracy.”
Mr Wilson’s decision to resign his membership as well as the party whip will reduce the first overall Scottish Parliament majority won by Mr Salmond in 2011 to a margin of one.
There are currently 128 MSPs at Holyrood, one less than the 129 who were elected in 2011 following the death of Margo MacDonald earlier this year. Her seat will remain vacant until the next election.
Tricia Marwick, who was elected as an SNP representative, resigned from the party to take up her post as Presiding Officer. In that role, she does not vote unless it there is a tie and she must cast the deciding ballot.
Out of 127 MSPs effectively sitting, which excludes Ms Marwick, the SNP now has 64 – enough for a majority of one.
The SNP lost two of the original 69 MSPs elected in the party’s 2011 landslide victory, when John Finnie and Jean Urquhart quit after the party voted to scrap its opposition to Nato at its 2012 conference.
Mr Salmond’s Holyrood majority was further depleted when Bill Walker was expelled from the SNP after he was convicted of assaulting his former wives and jailed for 12 months.
Mr Wilson’s resignation came hours before nominations open today for the leadership of the SNP, following Mr Salmond’s announcement that he will stand down after the referendum defeat. Mr Salmond’s deputy, Nicola Sturgeon, is expected to be appointed to the role unchallenged.
Mr Wilson, a graduate of Glasgow University and a former director of Scotland’s low pay unit, joined the SNP in 1999. He was a North Lanarkshire councillor between 2007 and 2009 but stood down to concentrate on his Holyrood responsibilities.
He is a member of the Scottish Parliament’s local government and communities committee and of the public petitions committee.
Last night, a spokesman for the SNP said: “We wish Mr Wilson well and accept his decision – which of course comes at the same time as more than 26,000 people have joined the SNP in recent days, overtaking the Lib Dems UK-wide and over doubling our membership. The SNP continues to have a majority in the Scottish Parliament.”