The Prime Minister warned that the economic impact of Brexit would hit jobs and opportunities for years to come.
“These are risks to our families and we should not take them,” he said.
He warned that “future generations” would be “hit hardest” in a hastily-arranged speech outside 10 Downing Street.
Mr Cameron said: “For you, for your family, for the future of our country, vote Remain.”
Opinion polls have suggested that older voters are more likely to back Brexit and Mr Cameron addressed them directly.
He said: “I want to speak very directly to those of my generation and older. I know Europe isn’t perfect, believe me I understand and I see those frustrations. I feel them myself.
“That’s why we negotiated and enhanced our special status - out of the euro, keeping our borders, not involved in ever closer union. We have the best of both worlds.
“So as you take this decision, whether to remain or leave, do think about the hopes and dreams of your children and grandchildren. They know their chances to work, to travel, to build the sort of open and successful society they want to live in rests on this outcome.
“And remember, they can’t undo the decision we take. If we vote out, that’s it. It is irreversible. We will leave Europe for good.
“The next generation will have to live with the consequences far longer than the rest of us.”
On Thursday “it will just be you in that polling booth”, he said, “taking a decision that will affect your future, your children’s future, your grandchildren’s future”.
He said: “Our economic security is paramount. It will be stronger if we stay; if we leave we will put it at risk.
“That is a risk to jobs, a risk to families, a risk to our children’s future and there is no going back.”
Steve Hilton, David Cameron’s former policy guru and Leave supporter, labelled the statement given by the Prime Minister as “weird”.
He told BBC News: “It was very interesting actually and rather an amazing thing to hear because what you just saw from the Prime Minister was an admission that they have lost the economic argument, they have lost the argument on immigration and so he has been wheeled out by rather panicky spin doctors, it seems to me, to try and change the subject.”