Let $X\subseteq \{1,\dots,k\}^{\mathbb Z}$ be a subshift over a finite alphabet, let $T$ be the shift, and let $\mu$ be an ergodic $T$-invariant probability measure. Fix an effective coding of finite words over $\{1,\dots,k\}$ into binary strings, and let $K_{\mathrm{pf}}(w)$ denote prefix-free Kolmogorov complexity of the coded word, measured in nats. If $h_\mu(T)$ denotes the Kolmogorov-Sinai entropy of the shift, computed with natural logarithms, then for $\mu$-a.e. $x\in X$, \begin{align*} \liminf_{n\to\infty}\frac{1}{n}K_{\mathrm{pf}}(x_0x_1\cdots x_{n-1}) = \limsup_{n\to\infty}\frac{1}{n}K_{\mathrm{pf}}(x_0x_1\cdots x_{n-1}) =h_\mu(T) \end{align*} so the full limit exists and equals $h_\mu(T)$. Changing the universal prefix-free machine, after fixing a standard effective finite-word coding, changes $K_{\mathrm{pf}}$ by $O(1)$ and therefore does not affect the limit. If complexity is measured in bits, the right-hand side is $h_\mu(T)/\log 2$.