  Suppose $(\mathcal{C},\mathbb{E},\mathfrak{s})$ is an $n$-exangulated
category. We show that the idempotent completion and the weak idempotent
completion of $\mathcal{C}$ are again $n$-exangulated categories. Furthermore,
we also show that the canonical inclusion functor of $\mathcal{C}$ into its
(resp. weak) idempotent completion is $n$-exangulated and $2$-universal among
$n$-exangulated functors from $(\mathcal{C},\mathbb{E},\mathfrak{s})$ to (resp.
weakly) idempotent complete $n$-exangulated categories. Furthermore, we prove
that if $(\mathcal{C},\mathbb{E},\mathfrak{s})$ is $n$-exact, then so too is
its (resp. weak) idempotent completion. We note that our methods of proof
differ substantially from the extriangulated and $(n+2)$-angulated cases.
However, our constructions recover the known structures in the established
cases up to $n$-exangulated isomorphism of $n$-exangulated categories.
