We give a generalization for Jordan algebras of the ical Liouville theorem describing the conformal transformations of a euclidean vector space. In a first step we establish an infinitesimal version which is purely algebraic ; namely, we show that the structure Lie algebra of a simple Jordan algebra (not isomorphic to $\mathbb R$ or $\mathbb C$) is of finite order $2$. In a second step, using only elementary calculus and Lie theory, we deduce the global version describing the transformations of a simple Jordan algebra which are conformal with respect to the structure group of the Jordan algebra. It turns out that these transformations form a Lie group of birational transformations, also known as the Kantor-Koecher-Tits group, and we can characterize this group as the group of conformal transformations of the conformal closure of the Jordan algebra.