Two semigroups are distinct if they are neither isomorphic nor anti-isomorphic. Although there exist 15973 pairwise distinct semigroups of order six, only four are known to be non-finitely based. In the present article, the finite basis property of the other 15969 distinct semigroups of order six is verified. Since all semigroups of order five or less are finitely based, the four known non-finitely based semigroups of order six are the only examples of minimal order.