  Given a von Neumann algebra $M$ denote by $S(M)$ and $LS(M)$ respectively the
algebras of all measurable and locally measurable operators affiliated with
$M.$ For a faithful normal semi-finite trace $\tau$ on $M$ let $S(M, \tau)$
(resp. $S_0(M, \tau)$) be the algebra of all $\tau$-measurable (resp.
$\tau$-compact) operators from $S(M).$ We give a complete description of all
derivations on the above algebras of operators in the case of type I von
Neumann algebra $M.$ In particular, we prove that if $M$ is of type I$_\infty$
then every derivation on $LS(M)$ (resp. $S(M)$ and $S(M,\tau)$) is inner, and
each derivation on $S_0(M, \tau)$ is spatial and implemented by an element from
$S(M, \tau).$
