The concept of regularity in $\Gamma$-semigroups is not very easy to deal with even though it shares some analogy with its analogue in semigroup theory. In this paper we establish a mechanism which translates the regularity in a $\Gamma$-semigroup $(S,\Gamma)$ as the usual von Neumann regularity in an ordinary semigroup $\Omega_{\gamma_{0}}$ that we construct in terms of $(S,\Gamma)$. This enables us to characterize the regularity in $\Gamma$-semigroups by means of quasi-ideals. A similar characterization is proved for those $\Gamma$-semigroups which are regular and intra-regular.