Lord Malloch-Brown, who served in the Foreign Office under Gordon Brown for two years, said Scotland had an "historically better relationship with Europe than many other parts of the UK".
For that reason, he said he believed the country would be "welcomed to the table in Brussels" if it did vote to leave the UK in next year's referendum.
He also claimed Europe could have "bigger problems" with the rest of the UK, with Prime Minister David Cameron proposing a referendum on EU membership if the Tories are returned to power in the 2015 general election.
Lord Malloch-Brown, who was previously deputy secretary general of the United Nations (UN), told BBC Scotland: "Continental Europe does not view its problem as being with Edinburgh, but with London."
He also appeared to suggest an independent Scotland would be able to become a member of the UN, but warned if the country left the UK it could lose some of its influence in such international organisations.
The former senior diplomat said: "Frankly, the underlying issue that Scotland has to reflect on is that probably it can get into all these organisations with relative ease, but it may in many of them have a diminished voice versus when it was part of the broader United Kingdom, and it is going to have to make that choice.
"The real question for Scots is do we have a bigger voice in the world as part of the United Kingdom or speaking with a more authentic Scottish voice on international affairs, and I think that is the real choice that matters."
On the issue of an independent Scotland's membership of the EU, he said: "I don't think they would have any particular reason to want to make things tricky for Scotland.
"I think the fact that Scotland would likely remain very pro-European would mean they would be anxious to embrace Scotland and bring it in, so if they were going to make the issue embarrassing for anybody it is more likely they would make it embarrassing for London, with whom they have bigger problems.
"My own guess is whatever the legal formalities, in terms of the political will if Scotland were to vote for independence, I think Europe would try to smooth its way into taking its place as a European member."
Despite that, he said there could be "problems", including the "issue of what does Scotland inherit in terms of rights to a seat at the table in Brussels".
But he insisted: "I still think Scotland has always had this historically better relationship with Europe than many other parts of the UK, and I anticipate it would be welcomed to the table in Brussels."
Lord Malloch-Brown added that for some "the idea of keeping Scotland but losing the rest of Britain would be a consolation prize of sorts, but it certainly wouldn't make up for the major loss".
But he also appeared to suggest membership of the UN would not be a problem, saying the international organisation was "very used to bringing in states".
He added: "Not that many things work smoothly in the UN but the addition of a new member is something they've had a lot of practice at."
His comments were welcomed by Blair Jenkins, chief-executive of the pro-independence campaign group Yes Scotland.
Mr Jenkins said: "Here we have yet another very senior and experienced diplomatic authority expressing the very clear view that an independent Scotland will be made very welcome in the EU as well as other international organisations.
"Mr Malloch-Brown is also underlining what we have always said - that an independent Scotland will take up its rightful place in the international community and play a key role within it."
SNP MSP Annabelle Ewing, a member of Holyrood's Referendum Bill Committee, said: "These sensible comments from a former UK Labour government minister completely back up the position of the Scottish Government that an independent Scotland will be 'welcomed to the top table in Brussels', as he himself puts it."
She added: "Mark Malloch-Brown served in government alongside Alistair Darling, so these comments are hugely embarrassing to the No campaign which he chairs."
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