In the literature, many of the descriptions of different classes of Leibniz algebras \((L, [\cdot , \cdot ])\) have been made by giving the multiplication table on the elements of a basis \({{\mathcal {B}}}=\{v_{k}\}_{k \in K}\) of L, in such a way that for any \(i,j \in K\) we have that \([v_i,v_j] = \lambda _{i,j} [v_j,v_i]\in {{\mathbb {F}}} v_k\) for some \(k \in K\), where \({{\mathbb {F}}}\) denotes the base field and \(\lambda _{i,j} \in {{\mathbb {F}}}\). In order to give an unifying viewpoint of all these classes of algebras, we introduce the more general category of Leibniz algebras admitting a multiplicative basis and study its structure. We show that if a Leibniz algebra L admits a multiplicative basis, then it is the direct sum \(L=\bigoplus \nolimits _{\alpha }{{{\mathcal {I}}}}_{\alpha }\) with any \({{\mathcal {I}}}_{\alpha }\) a well-described ideal of L admitting a multiplicative basis inherited from \({\mathcal {B}}\). Also the \({{\mathcal {B}}}\)-simplicity of L is characterized in terms of the multiplicative basis.