In a planned transition, Smee will continue to head up UK Youth until the end of the year while the youth charity searches for her replacement.
As chief executive of the YFF, Smee will be responsible for distributing £90m of dormant assets to groups that tackle youth unemployment, including public, private and voluntary sector groups.
The foundation, launched by the former civil society minister Mims Davies in March, aims to "remove the barriers preventing disadvantaged young people from entering the labour market", and is set to have a specific focus on addressing the ethnic disparities in youth unemployment.
In 2017, Smee oversaw the merger of UK Youth and Ambition, and has been credited with increasing the charity's reputation and financial stability since joining in 2014.
Smee said: "The five years I've spent with the charity have been some of the best of my life. It has been an honour to work with so many inspiring young people and dedicated youth workers and volunteers. I will be very sad to leave.
"The sector needs UK Youth to remain a strong and passionate advocate for youth work and young people."
UK Youth's chair, Lady Anne Stoneham, added: "Over the past five years, Anna has been an inspirational, passionate and enthusiastic leader of UK Youth and is incredibly well-respected throughout the youth sector. We will be very sad to see her go but are delighted at the successes she has achieved for the charity."
The charity said recruitment for Smee's replacement will begin immediately.