Graham Avery's intervention was seized on by pro-independence campaigners as evidence there will be a smooth transition to Scottish statehood after a Yes vote in 2014.
It is the latest twist in the row sparked by the Scottish Government's admission that no specific legal advice has been taken on the country's position in the EU in the event of independence.
Opponents insist it is just as likely that Scotland would be forced to ask to rejoin and have to adopt the euro in place of the pound.
Comment by Stephen Noon, senior strategist with Yes Scotland
Mr Avery, also a senior adviser at the European Policy Centre in Brussels and senior member of St Antony's College, Oxford University, gave his view in written evidence to a Westminster inquiry on the foreign policy implications of Scottish independence.
"For practical and political reasons the idea of Scotland leaving the EU, and subsequently applying to join it, is not feasible," he wrote.
"From the practical point of view, it would require complicated temporary arrangements for a new relationship between the EU (including the rest of the UK) and Scotland (outside the EU), including the possibility of controls at the frontier with England. Neither the EU (including the rest of the UK) nor Scotland would have an interest in creating such an anomaly.
"From the political point of view, Scotland has been in the EU for 40 years and its people have acquired rights as European citizens. If they wish to remain in the EU, they could hardly be asked to leave and then reapply for membership in the same way as the people of a non-member country such as Turkey.
"The point can be illustrated by considering another example: if a break-up of Belgium were agreed between Wallonia and Flanders, it is inconceivable that other EU members would require 11 million people to leave the EU and then reapply for membership."
There are no clear precedents for Scottish independence in Europe and that transition would need to be in place before actual independence, he notes. This could take no more than two years from the referendum.
The British budget rebate could require "difficult negotiations" between Edinburgh and London, as well as Brussels.
Blair Jenkins, chief executive of the Yes Scotland independence campaign, said: "People in Scotland should be reassured that an independent Scotland will remain a member of the European Union. Not only that but, as Mr Avery points out, there may be opportunities for an independent Scotland, with a full voice and vote in the EU, to emerge with a better deal than is currently available as a member of the UK."
A European Commission spokewoman said: "It is not the role of the commission to express a position on questions of internal organisation related to the constitutional arrangements in the member states."
The EU row picked up pace on Tuesday last week when Deputy First Minister Nicola Sturgeon revealed to MSPs that no specific legal advice exists.
Labour accused First Minister Alex Salmond of being a "barefaced liar", insisting the SNP leader gave the impression in a television interview that advice did exist to back the assertion that Scotland would automatically remain in the EU.
Last night former Labour first minister Henry McLeish said Mr Salmond did not mislead the public. "I don't think he's misled," he told STV.
"I think it's easy to sit apart from the big decisions that have to be made in government, but he certainly hasn't handled the situation well."
Mr McLeish said the public is "sick and tired" of tribalism in politics.
Annabelle Ewing, an SNP member of Holyrood's Referendum Bill Committee, said: "These insightful comments by a former Labour first minister come as a breath of fresh air in Scottish politics where the opposition seem intent on smearing the First Minister and determined to avoid a real debate on Scotland's future."
Liberal Democrat leader Willie Rennie said Mr Avery's submission shows there is still doubt over currency, the Schengen free travel agreement and other treaty obligations.
"There are contradictory views including from the Spanish foreign minister who doubts Scotland's automatic membership. Even SNP MSP John Mason said this week, 'we are not in definitive territory'," he said.
"This has never been about whether Scotland would be excluded from the European Union. It's about the terms on which we would be a member. An independent Scotland could be forced to join the euro, accept Schengen and lose the rebate. That's why the Scottish Government have a duty to remove the doubt and secure the agreement of all the EU nations before the referendum.
"We can't just wait until 2015 to discover if the Spanish will use a veto. Otherwise the SNP is asking Scots to vote for independence in the dark."
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