In a letter to Holyrood's Presiding Officer Ken Macintosh, the MEPs and parliamentarians also say that the holding of a second referendum should be one for Scotland alone and tell Westminster not to stand in the way.
Parliamentarians from Germany, France, Italy, Spain, Belgium, Sweden, Greece and Malta, pledged their “full support” for Scotland’s membership of the EU after a vote for independence in a second referendum.
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"The question of Scotland’s constitutional future, and your relationships with the UK and the EU are for the people of Scotland to decide", the cross-party appeal states.
The letter seen by the Sunday Herald promises to help an independent Scotland with a “swift, smooth, and orderly” application for EU membership.
Backers of the appeal include Miriam Dalli, a Socialist MEP from Malta, Greek Green MP Giorgos Dimaras, André Gattolin – an ecologist Senator in the French parliament – and María Rosa Martínez Rodríguez, an 'Ecofeminist' member in the chamber of deputies in the Spanish Parliament.
However, there is also support from Swedish Centre Party MEP Fredrick Federley, Tanja Fajon, a Slovenian Social Democrat MEP and Barbara Matera, an Italian MEP for the centre-right People of Freedom (PdL) party.
The intervention will be seen as a major fillip for the First Minister and independence supporters who want Scotland to remain in the EU, an issue that could be a major bone of contention in a second referendum campaign.
However, the 50 European politicians directly contradict the claims made by the UK Tory leader, who has now trigged Article 50, the formal process for leaving the EU.
In their letter to Macintosh they accuse the Prime Minister of failing to "properly take into account the preferences of Scottish citizens in the withdrawal process".
They say: “We regret that the UK's government has chosen to follow the path of a 'hard Brexit' and has so far refused to properly take into account the preferences of Scottish citizens in the withdrawal process.
"Therefore, if Scotland were to become an independent country and decided to seek to maintain European Union membership, we offer our full support to ensure the transition is as swift, smooth, and orderly as possible.
"Scotland would be most welcome as a full member of the European Union, with your five million European citizens continuing to benefit from the rights and protections we all currently enjoy.”
In what will be seen as a dig at pro-Brexit politicians, the letter goes on to praise Scotland's "support for a Europe which is united in pursuit of progress and not divided by fear and self-interest" following its overwhelming vote to Remain in last year's referendum.
Downing Street has ruled out Nicola Sturgeon’s plans for a new second independence referendum before the UK is scheduled to leave, the EU in March 2019.
However, the signatories of the letter to Macintosh say that Scots should be free to make their own decision about any referendum.
They say: "We recognise that this was not your choice however and that Scotland voted strongly to remain within the EU.
"The question of Scotland’s constitutional future, and your relationships with the UK and the EU are for the people of Scotland to decide. It is not our place to tell Scotland what path you should take."
The letter, an initiative by West of Scotland Green MSP Ross Greer and German Green MEP Terry Reintke, is signed by parties from across the political spectrum from the EU Parliament, national and regional parliaments, assemblies and senates.
Greer, the Greens’ external affairs spokesperson, said the intervention showed how the only way Scotland could secure EU membership was to vote for independence.
He said: “With continuing uncertainty and an absolute lack of any clear plan from the UK government, what’s becoming clear is that there is a tremendous amount of goodwill from across the continent towards Scotland’s European aspirations.
"People in Scotland were told to vote against independence if they wanted to stay in the EU and now we know how wrong that was. Independence is the only way to secure a European future for Scotland.
"Furthermore, we were told that Spain would block an independent Scotland’s bid for EU membership and that we’d face being placed at the back of a mythical queue. Now we know that those No campaign arguments are not true.
"The only thing standing in Scotland’s way to forging links with Europe is the Westminster government.
"Our parliament has voted to give the people a choice over their own future and no Tory government at Westminster should stand in the way of that.”
German MEP Reintke, echoing the comments, said:“The inflammatory language we have witnessed, just one week after the official triggering of Article 50, is shocking and incredibly sad. Now should be the time to seek common ground, not stir up hatred and division.
"The question of Scotland’s constitutional future and its relationship with the EU is for the people in Scotland to decide.
"Irrespective of what they choose to do, we want to send a strong, cross-party, cross-national message that the the door to a common European future remains open.”