First of all, that usually mispelled last name.
LeBeouf is a French term for 'The Beef.' Shia -- Hebrew for 'gift from God,' while we're on the subject -- was born in Los Angeles to a rather tripped out family.
His mother Shayna is a ballerina turned jewellery designer, while his father Jeffrey is a Vietnam War veteran who happened to be a bit of a hippie and a drifter, working as a rodeo clown and a circus mime.
It made for quite the biopic-worthy childhood. Jeffrey used to grow cannabis and smoked marijuana with Shia when he was only ten, and after serious problems with heroin addiction, eventually divorced Shayna. Shia grew up with his mother, then, in rather cash-strapped environs.