  Given a type I von Neumann algebra $M$ with a faithful normal semi-finite
trace $\tau,$ let $L(M, \tau)$ be the algebra of all $\tau$-measurable
operators affiliated with $M.$ We give a complete description of all
derivations on the algebra $L(M, \tau).$ In particular, we prove that if $M$ is
of type I$_\infty$ then every derivation on $L(M, \tau)$ is inner.
