We provide complete characterisations for the compactness of weighted composition operators between two distinct $L^{p}$ -spaces, where $1\leq p\leq \infty$ . As a corollary, when the underlying measure space is nonatomic, the only compact weighted composition map between $L^{p}$ -spaces is the zero operator.

Let $u$ and $\unicode[STIX]{x1D711}$ be two analytic functions on the unit disc $D$ such that $\unicode[STIX]{x1D711}(D)\subset D$ . A weighted composition operator $uC_{\unicode[STIX]{x1D711}}$ induced by $u$ and $\unicode[STIX]{x1D711}$ is defined by $uC_{\unicode[STIX]{x1D711}}f:=u\cdot f\circ \unicode[STIX]{x1D711}$ for every $f$ in $H^{p}$ , the Hardy space of $D$ . We investigate compactness of $uC_{\unicode[STIX]{x1D711}}$ on $H^{p}$ in terms of function-theoretic properties of $u$ and $\unicode[STIX]{x1D711}$ .