The call, by six chiefs of leading youth sector organisations, including the National Youth Agency, UK Youth and Girlguiding, comes after the UK voted to leave the EU in last Thursday's referendum.
In a joint statement, the organisations warned the vote to leave the EU will "inevitably impact the lives of young people and the youth sector" but urged young people to take the "dramatic shift" as an invitation to get more involved in decision-making processes.
"This is the time for the next generation to shape the future of the UK," the statement reads.
"This is a once in a lifetime opportunity for young people on all sides of the debate to start painting a picture of the country they want the UK to become.
"We are calling on politicians and policymakers to fully and meaningfully engage young people at every level of their discussions over the next few months to ensure their views are heard and acted upon.
"The youth sector has a vital role to play in providing safe spaces for these conversations to take place and we must continue to empower young people to take charge of their own lives, dream of a future they want and work hard to achieve it."
The six signatures included Paul Miller of the NYA; Anna Smee, chief executive of UK Youth; Chris Martin, chief executive of The Mix; Jessica Taplin, chief executive of vInspired; Julie Bentley, chief executive of Girlguiding; and Thomas Lawson of Leap Confronting Conflict.
Overall, UK citizens backed leaving the EU by 51.9 per cent to the remain vote's 48.1 per cent, but YouGov data shows 75 per cent of young people aged 18 to 24 voted to remain.
The youth leaders said they hope all young people, regardless of their decision, and those who were also too young to vote, will recognise "this pivotal moment".
"We are calling on young people to be bold and to set out a new vision for the UK that will benefit them and our wider society over the decades to come," it adds.