The former prime minister will make the prediction when he joins the fight to keep the United Kingdom in the EU during an event in Edinburgh.
In a series of interventions ahead of David Cameron’s in/out referendum, Mr Brown will speak at the inaugural meeting of the Scottish Labour Movement for Europe.
He will call for the UK to resist becoming a “bit-part player” by voting to exit, as he emphasises the economic benefits of EU membership to Scots, and rejects arguments that there are “plus points for safety” by leaving.
Opinion polls suggest the outcome of the Prime Minister’s vote – which could be held as early as the summer – is on a knife-edge.
A poll conducted by Survation last month showed 51% of people across the UK want to leave the EU, while 49% wish to stay.
The survey found 42% of Scots want to leave, while 58% would vote to stay.
The figure mirrors the Scottish vote in the 1975 referendum on Europe, but Mr Brown believes an even higher majority can be achieved in the forthcoming ballot.
He will say: “I believe we can do much better in 2016, and if we put forward a positive, principled and progressive case, we can win 70% for versus 30 against.”
He will continue: “We must start this debate from the needs and aspirations of Britain’s working families – not institutions and constitutions – and make the case for exactly what kind of country we want to be.
“This referendum should be about jobs, security and the future prospects of our young.
“We must be positive by showing, as the research from the Centre for Economics and Business states, that up to 300,000 Scottish jobs are linked to membership of the European Union and
20,000 Scottish businesses trade with mainland Europe.
“What’s more is that 1,000 Europe-owned businesses are Scots employers, and 46% of Scots international exports go to Europe.
“We must be principled showing we do best not just as members of Europe but as leaders of Europe.”
Mr Brown will add: “There is a stronger, patriotic view of Britain’s best future that is different from those who glory in us standing apart and want us to be wholly separate, defiantly independent of others.
“It is the patriotic vision that affirms that Britain is not the Britain we know unless we are outward-looking, unless we are engaged with the continent and unless British values – tolerance, liberty, fairness and social responsibility – play a leading role in shaping Europe and helping Europe to lead in the world.
“Our destiny can never be some kind of bit-part player semi-detached on someone else’s stage or a bystander hectoring from the wings. We must at all times be setting the agenda in Europe, bringing people together in Europe and championing change in Europe.”
On the one year anniversary of the attack on satirical publication Charlie Hebdo in Paris, and in light of the terror attacks in the city in November, Mr Brown will also say: “There are absolutely no plus points in safety from leaving.
“There are only potential gains in safety from enhanced co-operation, through the police, judiciary and military, to root out terrorists.
“We can only be sure that there is no safe haven and no hiding place for terrorists anywhere by maximising co-operation with every country opposed to terrorism.”
He will conclude: “The real challenge is to convert an often inward-looking Europe, not into some federal super state – all the European nations that I have visited are proudly independent with their own traditions – but into an outward-looking, globally-oriented Europe with a reach and influence spanning every hemisphere.”
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