While 55% of those who voted backed Scotland remaining in the UK, the debate sparked a massive interest in politics, recording the highest every turnout in any UK ballot.
SNP business convener Derek Mackay said many of those who had joined the party since the referendum would be new to politics and would “continue the legacy of the referendum, and the amazing level of engagement we saw”.
The party claimed its membership now stood at 30,486, a rise of 4,884 from Thursday when it was 25,642.
Mr Mackay said: “Seeing our membership spike by nearly 5,000 is incredibly encouraging.
“Some will no doubt be coming from Labour - whose traditional heartlands were voting Yes on Thursday - but many will be new to politics, and they will continue the legacy of the referendum, and the amazing level of engagement we saw.”
The Scottish Green Party, which campaigned for independence, has also seen a rush of people signing up to become a member.
The party said more than 2,000 people have joined since polls closed on Thursday, peaking at a rate of four per minute.
Patrick Harvie, the party’s co-convener, said: “This spectacular increase in our membership shows that the hope and inspiration of the Yes campaign will not be fading away.
“We will be redoubling our efforts for a fairer, greener Scotland and will be doing so as a much larger force than we were a few days ago. The referendum campaign has transformed Scotland and it is no exaggeration that it has transformed the Scottish Green Party as well.”