The absence of millions of young voters from the electoral register could lead to a victory for the Leave camp in the EU referendum, he warned.
Mr Miliband said their “optimistic generation” can keep Britain in the EU.
But Leave campaigner, Conservative MP James Cleverly, said Mr Miliband’s “cynical” comments would “fool no-one”.
‘Young can decide’
Mr Miliband said in a speech in London on Saturday that 1.5 million of the six million 18-24 year olds eligible to vote are not registered, nor are a quarter of the eight million 25-35 year olds.
They have until 7 June to register to vote in the UK’s referendum on its membership of the EU, which takes place on 23 June.
Mr Miliband said: “Today is a call to arms to all young people to register to vote.
“Let’s be clear about the danger – a decision not to vote is a decision to let someone else decide your future.
“Young people can decide this referendum. If they don’t use their vote, the danger is this referendum will be lost.”
Mr Miliband, who resigned as leader of the Labour Party following its defeat in the 2015 general election, said the Leave side offered a “narrow” future which pretended to be about national freedom.
He added: “When the Leave campaign is asked about the future – future jobs, future opportunities, future growth – they have one answer: they just don’t know.
“Those words should ring in the ears of every child, student and parent. Not knowing is not a path to prosperity, not knowing is the road to recession.”
Mr Miliband also told BBC Breakfast that polls suggested younger people were more likely to vote to remain in the EU by three to one, and that older people should “heed the wisdom of the young”.
He added: “All round the world young people are kicking against the establishment, and yet young people want to back Remain.
“That shows Remain is a future-orientated, positive, optimistic idea, because I think young people take for granted that we’ve got to work with other countries, and not isolate ourselves.”
Mr Cleverly said Mr Miliband’s “cynical” attempt to reach young people “will fool no-one”.
“After his failed efforts to court the youth vote via Russell Brand last year, you’d think he would know better.”
He also told the BBC that he “absolutely” wanted young people to vote in the referendum.
“When I talk to young people, actually I find that they are very concerned about the costs of EU membership, about how it limits our ability to trade with the developing world, and how it impinges on our democracy.”
Meanwhile, David Cameron indicated he still regards Leave campaigner Boris Johnson as a “substantial” potential future successor, despite the former London mayor’s increasingly personalised battle with the prime minister over Britain’s future in Europe.
Mr Cameron said he would not reconsider comments he made that Mr Johnson, George Osborne and Theresa May were all figures who could step into his shoes when he steps down, which he has promised to do before the next general election.