The athlete, who is a Goodwill Ambassador for the United Nations Children's Fund (UNICEF), will deliver a letter signed by stars including Claudia Schiffer, Whoopi Goldberg and Robbie Williams calling for an end to hunger for youngsters.
The sportsman will discuss the issue of stunting in children - when they do not have a balanced diet early on in life - which can lead to brain damage, and he has called on Cameron to highlight the issue as London prepares to host the 2012 Olympics.
Beckham says, "Stunting - when children don't get the right nutrients in the first 1,000 days of life - is the hidden crisis stopping millions of children around the world reaching their potential. It's irreversible. It means children get trapped in lives of poverty.
"During the coming weeks all eyes will be on London for the greatest show on earth. As a UNICEF Ambassador, I am asking the Prime Minister to use the global spotlight on our nation to make children around the world the real winners of these Games."