John Finnie, 55, and Jean Urquhart, 63, announced their decision at Eden Court in Inverness, describing it as “heart-wrenching”.
The pair are long time members of the party and were elected to Holyrood as list members for the Highlands and Islands at the last elections in 2011.
They were both outspoken critics of the move to continue Nato membership and were among eight MSPs who led a grassroots revolt against the party leadership's plan to take an independent Scotland into the nuclear armed military alliance.
They will now sit in the Scottish Parliament as independents.
Mr Finnie, who first joined the party when he was 16, said: “I understand that there are those who wish to stay within the SNP and to continue to fight our corner in this essential debate, and I accept their reasons for doing so.
“However, I cannot continue to belong to a party that quite rightly does not wish to hold nuclear weapons on its soil, but wants to join a first strike nuclear alliance.
“Although I envisage that I will continue to share common ground with the SNP on many issues, I cannot in good conscience continue to take the party whip.”
Jean Urquhart, who has been a supporter of independence for 25 years and a CND member for 35 years, added:
“The issue of nuclear disarmament and removing Trident from Scotland’s waters is a red line issue for me, and I could not remain committed to a party that has committed itself to retaining membership of NATO.
“We are both steadfast in our belief that Scotland should be an independent country, and will actively and positively campaign for a Yes vote in 2014.
“We believe in an independent Scotland, not a NATO-dependent Scotland.
“John and I will continue to work with MSPs across the Chamber for a fairer and more peaceful Scotland.
“Importantly, we look forward to continuing to represent the residents of the Highlands and Islands as we have done since May 2011.”
Their decision to leave the party will not affect the SNP’s majority in the Scottish Parliament.
SNP leader Alex Salmond said: "I'm saddened that Jean and John have decided to resign from the party.
"They have been excellent servants to the SNP, and I'm grateful to them for their tireless efforts.
"We had an excellent and democratic debate at party conference last Friday, and agreed a policy of reaffirming our opposition to nuclear weapons as a non-nuclear member of the Nato alliance - a position that will be accepted by the party as a whole.
"Jean and John have indicated to me that they will continue to support the Government from the back benches, and I welcome that.
"I also look forward to working with them both in the campaign to achieve a Yes vote in Scotland's referendum in 2014."
The SNP narrowly voted to abandon its long-standing opposition to Nato at its conference in Perth last week.
The move, which was backed by the party hierarchy, received a majority of just 29 votes, with delegates voting 394 to 365 to reject an amendment by rebel MSPs and party members that would have reaffirmed the SNP’s anti-Nato stance, against the wishes of First Minister Alex Salmond and defence spokesman Angus Robertson.
Mr Robertson's new pro-Nato policy was finally approved by 426 votes to 332.
The u-turn means that the SNP will now apply to keep Scotland in Nato if it is elected to lead the first post-independence government.
Mr Robertson insists that Scotland will only remain in Nato on the condition that it will be allowed to remove nuclear weapons from the Clyde.
However, SNP rebels feared that Scotland will face pressure to retain them if it remains in Nato.
They have also raised concerns that an independent Scotland will be beholden to the interests of the USA and UK Governments.
The departure of Mr Finnie and Ms Urquhart reduces the SNP's post-2011 election roll at Holyrood from 69 MSPs to 65.
Mr Finnie now describes himself on social networking site Twitter as "Independent MSP for Highlands and Islands", appending the hashtag #notoNATO.
Ms Urquhart has changed her Twitter name from @JeanUrquhartSNP to @JeanUrquhartMSP.
Isobel Lindsay, vice-chair of the Scottish Campaign for Nuclear Disarmament, said: "Scottish CND have great respect for John Finnie and Jean Urquhart's integrity.
"We are sure that they will continue to work for a non-nuclear independent Scotland that is not part of an aggressive military alliance."
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