Mothers should vote for Britain to stay in the European Union for the sake of their children's future, Gordon Brown will say.
Around 500,000 new jobs can be created by opening up the single market further to British firms, according to the former Prime Minister.
Environmental cooperation across the 28-member bloc could lead to cuts in energy bills and Brussels has boosted protections for workers, he will also insist.
The EU is leading the way in rooting out tax havens and links between British and European forces are helping to stamp out terrorism, people smuggling and trafficking, the former premier will tell the Fabian Society summer conference.
He will issue a direct plea to more than nine million Labour voters as well as young people to turn out for the referendum on June 23.
"My message to young people is that Europe still is, and is more than ever, the future for jobs, environmental sustainability and fairness," Mr Brown will say.
"My message to mothers, worried about their children's future, is that the biggest job creator of the next decade will be Europe's single market.
"My message to those who feel globalisation is like an out-of-control runaway train is that only through cooperation – starting with the European Union – can we manage global change in an interdependent world in the public interest.
"This shows why the future is not 'Britain leaving Europe to join the world', as Brexit supporters say, but joining with the rest of Europe to lead in the world.
"The way forward lies in Britain leading in Europe, not leaving."
Mr Brown will tell Labour voters they should back Remain to "secure the jobs of the future" as he sets out a "positive" case for remaining part of the bloc.
He will say: "New jobs in digital, financial services and energy – areas in which Britain is a world leader – will match the jobs we have already secured in transport, aviation, food and drink and advanced manufacturing.
"The jobs of the future that will be created by the European single market will be among the highest-skilled and best-paying jobs that the next generation of young workers can obtain.
"In services alone, one estimate is that by 2030 we can deliver up to 480,000 jobs which include up to 120,000 jobs across the technical professional, information and communication and repair and servicing sectors, all areas where Britain is strong and can sell directly into European markets."
Mr Brown will also highlight the findings of a poll by campaign group Hope Not Hate showing that Labour supporters aged 18-30 want to stay in the EU by a margin of four to one, but will warn that many risk losing their right to vote.
"It is feared as many as half of Britain's young people may not vote. Some 30% of young people - twice the national average - are not registered to vote and many students registered at their college address risk losing the right to vote as they will not be there when ballot papers get sent out."