Alyn Smith said membership would not be a “whizz-bang, everything changes at midnight” event.
The MP said the Scottish Government would publish a “clear roadmap” for re-joining the EU, which “people will be able to kick the tyres of and understand fully”.
It comes after First Minister Nicola Sturgeon launched her updated economic case for independence on Monday. It said an independent Scotland would apply to re-join the EU and the Scottish Government "would put in place measures to smooth any checks required as a result of Brexit on goods moving to and from England and Wales".
Mr Smith, who is speaking at a Yes for EU rally in Edinburgh today, was asked about the practicalities of re-joining. He told The Scotsman: "You'll hear a lot of phasing in and phasing out. We'll be phasing out of UK stuff and phasing in to EU stuff.
"Now, all of those things don't happen simultaneously, all of those things don't happen at midnight on a particular date. There will be bits that we'll opt into as we're negotiating."
He added: "It's not a whizz-bang, everything changes at midnight on a particular night, different bits will be opted into as they're ready. Some things will take longer to negotiate. But meantime, what's most relevant to the citizens of our country, the businesses of our country, is that we'll get these rights back and we'll have a timetable that will need to be negotiated with the EU to get back in.
"There's a further paper coming out from the Scottish Government fairly soon about the EU aspects of the independence process, but as we did in 2014, we'll have a clear roadmap that people will be able to kick the tyres of and understand fully as that goes forward."
Mr Smith said: "The details and the nuts and bolts will come later, but I think everybody in Scotland recognises that there's no huge, insurmountable impediment to us getting back in. We were part of the EU for so long. The EU has accepted states in considerably worse nick than we are now, even with our current travails."